Math 125 Midterm 2 Answers printable pdf download

Math 125 Midterm 2 Answers

MIDTERM 2 ANSWERS

MATH 125

Problem 1.(13 points total) Compute the following integrals. Give your answer in exact form (do

not use decimals).

a.(6 points)

+ 2 + 1

Solution: partial fractions. Get

2 ln

+ 1 + 5

+ 1

ln(tan )

b.(7 points)

sin cos

(ln 3)

Solution: substitution! Guess:

= ln(tan ). Get

Problem 2.(8 points total) Compute the following integral. Give your answer in exact form (do not

use decimals).

+ 4

3 2

+ 4

Solution: trig substitution. Get

+ 4 +

Problem 3.(9 points total)

Find a postitive number

such that the average value of the function

( ) =

on the interval [0 ] equals 1.

Solution:

= 6.

Problem 4.(9 points)

Use Simpson’s Rule with

= 4 subintervals to approximate the integral

Solution: approximately 30 25

Problem 5.(11 points) Determine whether each of the following integrals is convergent or divergent.

If it is convergent, evaluate it.

2 + 3

a.(5 points)

+ 3 + 1

Solution: use substitution. Integral is divergent.

b.(6 points)

Solution: use integration by parts and L’Hospital’s rule. Integral is convergent and equal to 1.

Math 125 Midterm 2 Answers