httpwwwwebassignnetwebStudent Assignment -ResponsesJasPd Math 125 HW Ie

WebAssign Math 125 HW_1C (Homework)

Donald Marshall Math 125 Spring 2014 section A Spring 2014 Instructor Donald Marshall

Current Score - 80 Due Wednesday April 9 2014 1100 PM PDT

1 -5 pOints SCalcET752003MI

If f(x) = eX - 7 0 ~ x ~ 2 find the Riemann sum with n = 4 correct to six decimal p laces

taking the sample pOints to be midpoints

M4 = I I

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2 -6 points SCalcET7 52004

(a) Find the Riemann sum for f(x) = 6 sin x 0 ~ x ~ 31[2 with six terms tak ing t he sample

points to be right endpoints (Round your answers to six decimal places)

R6 = I I

(b) Repeat part (a) with midpoints as the sample points

M6 = I I

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3 -6 pOints SCalcET752007

A table of values of an increasing function f is shown Use the table to find lower and upper

130

estimates for f(x) dx 10

lower estimate

upper estimate

x 10 14 18 22 26 30

f(x) -13 -6 -3 1 3 8

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___w __ ________ __ __ ______ ___ ____ __ __ r _ _____ __ bull ___________ _ __ _ __ _ __ __ __ _ bullbull __ __ _ _ A __ __ _ _ _ __ _ __ _ ___ _ __ __ _ _ _ __ ___

4 -5 points SCalcET7 52009

Use the Midpoint Rule with the given value of n to approximate the integral Round the answer to

four decimal places

180

sin h dx n = 4

---------=--=1

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5 -5 points

Express the limit as a definite integral on the given interval

n lim ~ x In(2 + x2

) )x [2 4] n---gt oo ~ I I

i = 1

SCalcET752017 MI

dx

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2 of 10 432014 1057 AM

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6 -9 points SCalcET7 52034 MI

The graph of 9 consists of two straight lines and a semicircle Use it to evaluate each integral

y

--20

r - 10

0

(a)

(b)

(c)

1

r

-i

f lOJo g(x) dx

130

g(x) dx 10

f 35 Jo g(x) dx

y = g(x)

I

20 35

J

-V

x

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3 of 10 432014 1057 AM

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7 -5 pOints SCalcET7 5 2040

Evaluate the integral by interpreting it in terms of areas

118

o Ix - 91 dx

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8 -5 pOints SCalcET7 52 048 MI

If [5 f(x) dx = 14 and r5f(x) dx = 32 find [4 f(x) dxJ4 1 1

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4 of 10 432014 1057 AM

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9 -6 points SCalcETl 52054

Suppose f has absolute minimum value m and absolute maximum value M Between what two 8

values must 1f(x) dx lie

(smaller value)

(larger value)

Which property of integrals allows you to make your conclusion

If f(x) ~ 0 for a ~ x ~ b then [b f(x) dx ~ o

Ib o f(x) dx + f(x) dx = f(x) dxl

c

lb a c a

~ Ib If m ~ f(x) ~ M for a ~ x ~ b then m(b - a) f(x) dx ~ M(b - a)

a f(x) dx = 0[ ~ a

bl f(x) dx = -La f(x) dx

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5 of 10 432014 1057 AM

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10-6 pOints SCalcET7 52061

If m - f(x) - M for a - x - b where m is the absolute minimum and M is the absolute maximum

of f on the interval [a b] then

(bm(b - a) - Ja f(x) dx - M(b - a)

Use this property to estimate the value of the integral

lTr6

5 tan 2x dx Tr8

(smaller value)

(larger value)

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432 014 1057 AM6 of 10

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11-12 pOints

The equation

x2 l + = 1

16 9

defines an ellipse which is graphed above In this excercise we will approximate the area of this

ellipse

(a) To get the total area of the ellipse we could first find the area of the part of the ellipse lying

in the First Quadrant and then multiply by what factor I I

(b) Find the function y=f(x) that gives the curve bounding the top of the ellipse

(c) Use 1x= 1 and midpoints to approximate the area of the part of the ellipse lying in the First

Quadrant I I

Cd) Approximate the total area of the ellipse I ----------

7 of 10 432014 1057 AM

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12 -10 pOints

or th following pro lem the units of ria I re gl n

along wi h th uni s for a fun tiOD ( r tw fun tions) l ive he units of arh d wit in gral

(a) If is in c nd and I(x) is in ~ tro ondmiddot t h n1I( ) dr

In

t I t I fc t

b) If t is in liS ond d get is in fe t onds2 then [ g(t) dt

i in pound tis 2

fe t t c

pound ct middot

(c)Ifx in ~da andf(x) it tlearc F then 1 f(~drb

ISm

das

(g Fday

dcgr F

(d gr F) da

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(d) If X is in hours and 9(x) is in kil watts lit n f9(X) dx

in 1 il wa t

hour

kilowa llour

kil wa middot middothow

c) If L in In crs 1 and f (L) IS ill squar In ter l) hentJ(L)dL is in

m or

m ersshy

m

lim ers

f) If t is in minumiddot g(t) in gallonsfo and (t) is inI

fc minu b n 1 9(t) (t)dt is in

gallons

gallonsmlnut

(gallons middotminutes )foot

galla f )minu e

(g) If s in onds andJ )i in ~e c nd hen fmiddotU s) d

ill

pound 2 e 2

9 of 10 4320141057 AM

Math 125 HW Ie httpwwwwebassignnetlwebStuden tIAss ignment -Responseslastd

feetmiddot c

11 1 (h) If IS ill da and J(x) is in pounds then f(x) dr(I

is in Ipound

_ pound

da r p und

p und middotda

(i) If in in h Ji ) in squar in h and d( ) is in

p und per u i inch t h n [ A(x)d( oj dx is in

P un In h 82

P und lin hes

p un slin h

unds

(j) If 1 is in davs nd 1 ~) in fl u Me p r day h n

( U 1(1) dx i inJo

~ (Bu )d

flu cas

(fl u as )middotda

~ da I flu asc)

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