X2 t05 01 discs & washers (2012)
-
Upload
nigel-simmons -
Category
Education
-
view
1.225 -
download
2
Transcript of X2 t05 01 discs & washers (2012)
![Page 1: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/1.jpg)
Volumes of Solids rotationslice
Volumes By Discs & Washers
![Page 2: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/2.jpg)
Volumes of Solids rotationslice
About the x axis
Volumes By Discs & Washers
![Page 3: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/3.jpg)
Volumes of Solids rotationslice
About the x axis
Volumes By Discs & Washersy
x
xfy
![Page 4: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/4.jpg)
Volumes of Solids rotationslice
About the x axis
Volumes By Discs & Washersy
x
xfy
a b
![Page 5: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/5.jpg)
Volumes of Solids rotationslice
About the x axis
Volumes By Discs & Washersy
x
xfy
a bx
![Page 6: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/6.jpg)
Volumes of Solids rotationslice
About the x axis
Volumes By Discs & Washersy
x
xfy
a bx
y
x
![Page 7: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/7.jpg)
Volumes of Solids rotationslice
About the x axis
Volumes By Discs & Washersy
x
xfy
a bx
y
x
xf
![Page 8: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/8.jpg)
Volumes of Solids rotationslice
About the x axis
Volumes By Discs & Washersy
x
xfy
a bx
y
x
xf
2xfxA
![Page 9: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/9.jpg)
Volumes of Solids rotationslice
About the x axis
Volumes By Discs & Washersy
x
xfy
a bx
y
x
xf
2xfxA
xxfV 2
![Page 10: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/10.jpg)
Volumes of Solids rotationslice
About the x axis
Volumes By Discs & Washersy
x
xfy
a bx
y
x
xf
2xfxA
xxfV 2
b
axxxxfV 2
0lim
![Page 11: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/11.jpg)
Volumes of Solids rotationslice
About the x axis
Volumes By Discs & Washersy
x
xfy
a bx
y
x
xf
2xfxA
xxfV 2
b
axxxxfV 2
0lim
b
a
dxxf 2
![Page 12: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/12.jpg)
About the y axisy
x
xfy
![Page 13: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/13.jpg)
About the y axisy
x
xfy
c
d
![Page 14: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/14.jpg)
About the y axisy
x
xfy
c
dy
![Page 15: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/15.jpg)
About the y axisy
x
xfy
c
dy xy
![Page 16: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/16.jpg)
About the y axisy
x
xfy
c
dy xy yg
![Page 17: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/17.jpg)
About the y axisy
x
xfy
c
dy xy yg
2ygyA
![Page 18: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/18.jpg)
About the y axisy
x
xfy
c
dy xy yg
2ygyA
yygV 2
![Page 19: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/19.jpg)
About the y axisy
x
xfy
c
dy xy yg
2ygyA
yygV 2
d
cyyyygV 2
0lim
![Page 20: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/20.jpg)
About the y axisy
x
xfy
c
dy xy yg
2ygyA
yygV 2
d
cyyyygV 2
0lim
d
c
dyyg 2
![Page 21: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/21.jpg)
axisabout therotatedis axis the
and 4between area when thegenerated volume theFind e.g. 2
xxxyi
![Page 22: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/22.jpg)
axisabout therotatedis axis the
and 4between area when thegenerated volume theFind e.g. 2
xxxyi
x
24 xy
-2 2
y4
![Page 23: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/23.jpg)
axisabout therotatedis axis the
and 4between area when thegenerated volume theFind e.g. 2
xxxyi
x
24 xy
-2 2x
y4
![Page 24: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/24.jpg)
axisabout therotatedis axis the
and 4between area when thegenerated volume theFind e.g. 2
xxxyi
x
24 xy
-2 2x
y4
x
24 xy
![Page 25: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/25.jpg)
axisabout therotatedis axis the
and 4between area when thegenerated volume theFind e.g. 2
xxxyi
x
24 xy
-2 2x
y4
x
24 xy
224 xxA
![Page 26: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/26.jpg)
axisabout therotatedis axis the
and 4between area when thegenerated volume theFind e.g. 2
xxxyi
x
24 xy
-2 2x
y4
x
24 xy
224 xxA xxxV 42816
![Page 27: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/27.jpg)
axisabout therotatedis axis the
and 4between area when thegenerated volume theFind e.g. 2
xxxyi
x
24 xy
-2 2x
y4
x
24 xy
224 xxA xxxV 42816
2
2
42
0816lim
xxxxxV
![Page 28: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/28.jpg)
axisabout therotatedis axis the
and 4between area when thegenerated volume theFind e.g. 2
xxxyi
x
24 xy
-2 2x
y4
x
24 xy
224 xxA xxxV 42816
2
2
42
0816lim
xxxxxV
2
0
428162 dxxx
![Page 29: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/29.jpg)
axisabout therotatedis axis the
and 4between area when thegenerated volume theFind e.g. 2
xxxyi
x
24 xy
-2 2x
y4
x
24 xy
224 xxA xxxV 42816
2
2
42
0816lim
xxxxxV
2
0
428162 dxxx
2
0
53
51
38162
xxx
![Page 30: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/30.jpg)
axisabout therotatedis axis the
and 4between area when thegenerated volume theFind e.g. 2
xxxyi
x
24 xy
-2 2x
y4
x
24 xy
224 xxA xxxV 42816
2
2
42
0816lim
xxxxxV
2
0
428162 dxxx
2
0
53
51
38162
xxx
3units 15
512
05
323
64322
![Page 31: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/31.jpg)
3 line about the rotated is 3
and 4by enclosed area when thegenerated volume theFind 2
yyxyii
![Page 32: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/32.jpg)
3 line about the rotated is 3
and 4by enclosed area when thegenerated volume theFind 2
yyxyii
x24 xy
y4
3y
![Page 33: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/33.jpg)
3 line about the rotated is 3
and 4by enclosed area when thegenerated volume theFind 2
yyxyii
x24 xy
(-1,3) (1,3)
y4
3y
![Page 34: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/34.jpg)
3 line about the rotated is 3
and 4by enclosed area when thegenerated volume theFind 2
yyxyii
x24 xy
(-1,3) (1,3)x
y4
3y
![Page 35: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/35.jpg)
3 line about the rotated is 3
and 4by enclosed area when thegenerated volume theFind 2
yyxyii
x24 xy
(-1,3) (1,3)x
y4
x
3y
![Page 36: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/36.jpg)
3 line about the rotated is 3
and 4by enclosed area when thegenerated volume theFind 2
yyxyii
x24 xy
(-1,3) (1,3)x
y4
x
2
2
1343
xxy
3y
![Page 37: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/37.jpg)
3 line about the rotated is 3
and 4by enclosed area when thegenerated volume theFind 2
yyxyii
x24 xy
(-1,3) (1,3)x
y4
x
2
2
1343
xxy
221 xxA
3y
![Page 38: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/38.jpg)
3 line about the rotated is 3
and 4by enclosed area when thegenerated volume theFind 2
yyxyii
x24 xy
(-1,3) (1,3)x
y4
x
2
2
1343
xxy
221 xxA
xxxV 4221
3y
![Page 39: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/39.jpg)
3 line about the rotated is 3
and 4by enclosed area when thegenerated volume theFind 2
yyxyii
x24 xy
(-1,3) (1,3)x
y4
x
2
2
1343
xxy
221 xxA
xxxV 4221
1
1
42
021lim
xxxxxV
3y
![Page 40: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/40.jpg)
3 line about the rotated is 3
and 4by enclosed area when thegenerated volume theFind 2
yyxyii
x24 xy
(-1,3) (1,3)x
y4
x
2
2
1343
xxy
221 xxA
xxxV 4221
1
1
42
021lim
xxxxxV
1
0
42212 dxxx3y
![Page 41: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/41.jpg)
3 line about the rotated is 3
and 4by enclosed area when thegenerated volume theFind 2
yyxyii
x24 xy
(-1,3) (1,3)x
y4
x
2
2
1343
xxy
221 xxA
xxxV 4221
1
1
42
021lim
xxxxxV
1
0
42212 dxxx
1
0
53
51
322
xxx
3y
![Page 42: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/42.jpg)
3 line about the rotated is 3
and 4by enclosed area when thegenerated volume theFind 2
yyxyii
x24 xy
(-1,3) (1,3)x
y4
x
2
2
1343
xxy
221 xxA
xxxV 4221
1
1
42
021lim
xxxxxV
1
0
42212 dxxx
1
0
53
51
322
xxx
3units 15
16
051
3212
3y
![Page 43: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/43.jpg)
generated. volume theFind axis. line about the
rotated is and curves ebetween th area The 22
yyxxyiii
![Page 44: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/44.jpg)
generated. volume theFind axis. line about the
rotated is and curves ebetween th area The 22
yyxxyiii
y
x
2xy 2yx
![Page 45: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/45.jpg)
generated. volume theFind axis. line about the
rotated is and curves ebetween th area The 22
yyxxyiii
y
x
2xy
(1,1)
2yx
![Page 46: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/46.jpg)
generated. volume theFind axis. line about the
rotated is and curves ebetween th area The 22
yyxxyiii
y
x
2xy
(1,1)y
2yx
![Page 47: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/47.jpg)
generated. volume theFind axis. line about the
rotated is and curves ebetween th area The 22
yyxxyiii
y
x
2xy
(1,1)y
2yx
![Page 48: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/48.jpg)
generated. volume theFind axis. line about the
rotated is and curves ebetween th area The 22
yyxxyiii
y
x
2xy
(1,1)y
2yx
21
yx
![Page 49: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/49.jpg)
generated. volume theFind axis. line about the
rotated is and curves ebetween th area The 22
yyxxyiii
y
x
2xy
(1,1)y
2yx
21
yx 2yx
![Page 50: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/50.jpg)
generated. volume theFind axis. line about the
rotated is and curves ebetween th area The 22
yyxxyiii
y
x
2xy
(1,1)y
2yx
21
yx 2yx
222
21
yyyA
![Page 51: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/51.jpg)
generated. volume theFind axis. line about the
rotated is and curves ebetween th area The 22
yyxxyiii
y
x
2xy
(1,1)y
2yx
21
yx 2yx
222
21
yyyA
yyyV 4
![Page 52: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/52.jpg)
generated. volume theFind axis. line about the
rotated is and curves ebetween th area The 22
yyxxyiii
y
x
2xy
(1,1)y
2yx
21
yx 2yx
222
21
yyyA
yyyV 4
1
0
4
0lim
yyyyyV
![Page 53: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/53.jpg)
generated. volume theFind axis. line about the
rotated is and curves ebetween th area The 22
yyxxyiii
y
x
2xy
(1,1)y
2yx
21
yx 2yx
222
21
yyyA
yyyV 4
1
0
4
0lim
yyyyyV
1
0
4 dyyy
![Page 54: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/54.jpg)
generated. volume theFind axis. line about the
rotated is and curves ebetween th area The 22
yyxxyiii
y
x
2xy
(1,1)y
2yx
21
yx 2yx
222
21
yyyA
yyyV 4
1
0
4
0lim
yyyyyV
1
0
4 dyyy
1
0
52
51
21
yy
![Page 55: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/55.jpg)
generated. volume theFind axis. line about the
rotated is and curves ebetween th area The 22
yyxxyiii
y
x
2xy
(1,1)y
2yx
21
yx 2yx
222
21
yyyA
yyyV 4
1
0
4
0lim
yyyyyV
1
0
4 dyyy
1
0
52
51
21
yy
3units 103
051
21
![Page 56: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/56.jpg)
(iv) (1996) y
x1 4
1
-1
S02 yx
The shaded region is bounded by the lines x = 1, y = 1 and y = -1 and the curve . The region is rotated through about the line x = 4 to form a solid.
When the region is rotated, the line segment S at height y sweeps out an annulus.
02 yx 360
![Page 57: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/57.jpg)
a) Show that the area of the annulus at height y is equal to 78 24 yy
![Page 58: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/58.jpg)
a) Show that the area of the annulus at height y is equal to 78 24 yy
y
![Page 59: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/59.jpg)
a) Show that the area of the annulus at height y is equal to 78 24 yy
y r
![Page 60: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/60.jpg)
a) Show that the area of the annulus at height y is equal to 78 24 yy
y
R
![Page 61: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/61.jpg)
x1 4
1
-1
S02 yx
![Page 62: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/62.jpg)
x1 4
1
-1
S02 yx r
![Page 63: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/63.jpg)
x1 4
1
-1
S02 yx r3
14
![Page 64: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/64.jpg)
x1 4
1
-1
S02 yx r3
14
R
![Page 65: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/65.jpg)
x1 4
1
-1
S02 yx r3
14
R24
4yx
![Page 66: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/66.jpg)
a) Show that the area of the annulus at height y is equal to 78 24 yy
y
![Page 67: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/67.jpg)
a) Show that the area of the annulus at height y is equal to 78 24 yy
y
R24
4yx
![Page 68: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/68.jpg)
a) Show that the area of the annulus at height y is equal to 78 24 yy
y
r
R24
4yx
314
![Page 69: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/69.jpg)
a) Show that the area of the annulus at height y is equal to 78 24 yy
y
r
R24
4yx
314
222 34 yyA
![Page 70: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/70.jpg)
a) Show that the area of the annulus at height y is equal to 78 24 yy
y
r
R24
4yx
314
222 34 yyA
78
981624
42
yyyy
![Page 71: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/71.jpg)
b) Hence find the volume of the solid.
![Page 72: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/72.jpg)
b) Hence find the volume of the solid.
yyyV 78 24
![Page 73: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/73.jpg)
b) Hence find the volume of the solid.
yyyV 78 24
1
1
24
078lim
yyyyyV
![Page 74: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/74.jpg)
b) Hence find the volume of the solid.
yyyV 78 24
1
1
24
078lim
yyyyyV
1
0
24 782 dyyy
![Page 75: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/75.jpg)
b) Hence find the volume of the solid.
yyyV 78 24
1
1
24
078lim
yyyyyV
1
0
24 782 dyyy
1
0
35 738
512
yyy
![Page 76: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/76.jpg)
b) Hence find the volume of the solid.
yyyV 78 24
1
1
24
078lim
yyyyyV
1
0
24 782 dyyy
1
0
35 738
512
yyy
3units 15
296
0738
512
![Page 77: X2 t05 01 discs & washers (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042601/556f5e65d8b42a916b8b5108/html5/thumbnails/77.jpg)
b) Hence find the volume of the solid.
yyyV 78 24
1
1
24
078lim
yyyyyV
1
0
24 782 dyyy
1
0
35 738
512
yyy
3units 15
296
0738
512
Exercise 3A; 2, 5, 7, 9, 13, 14, 15
Exercise 3B;1, 2, 5, 7, 9, 10, 11, 12