CRMS Calculus 2010 May 14, 2010
-
Upload
colorado-rocky-mountain-school -
Category
Education
-
view
683 -
download
2
description
Transcript of CRMS Calculus 2010 May 14, 2010
![Page 1: CRMS Calculus 2010 May 14, 2010](https://reader033.fdocuments.net/reader033/viewer/2022052507/558bf61dd8b42a3d578b46d0/html5/thumbnails/1.jpg)
1
Area
Between
Curves
![Page 2: CRMS Calculus 2010 May 14, 2010](https://reader033.fdocuments.net/reader033/viewer/2022052507/558bf61dd8b42a3d578b46d0/html5/thumbnails/2.jpg)
2
Review:
1. a. State the numerical methods used to calculate the approximate value of the definite integral:
b. State the algebraic method used to calculate the exact value of the definite integral.
Calculus provides a way to find the exact area under a curve by slicing a region into strips, adding the
strips together and then taking the limit.
b
dx
Lengthis
constant
(x, y)
a
dA = y dx∫dAa
b
Area =
![Page 3: CRMS Calculus 2010 May 14, 2010](https://reader033.fdocuments.net/reader033/viewer/2022052507/558bf61dd8b42a3d578b46d0/html5/thumbnails/3.jpg)
3
1. Find points of intersection.
2. Slice region into vertical strips of width dx.
3. Show a representative strip and a sample point.
4. Write a differential (dA) representing the area of the strip.
5. Add up all the strips and take the limit as dx approaches 0.(In other words, integrate.)
![Page 4: CRMS Calculus 2010 May 14, 2010](https://reader033.fdocuments.net/reader033/viewer/2022052507/558bf61dd8b42a3d578b46d0/html5/thumbnails/4.jpg)
4
Method 1: Subtract areas (Gus' method):
Method 1: Integrate with respect to x: Method 1: Integrate with respect to y: