Name:
Section:
MATH 145
SAMPLE QUIZ 4
You may use a scientific calculator to complete this quiz. No notes please. Show all
work for full credit.
1. Evaluate the integral.
(a) Zx
x2+ 1 dx =1
2ln(x2+ 1) + C
(Why don’t we need the absolute value symbols around x2+ 1 in the answer?)
(b) Z1
0
xe−x2dx =1
21−
1
e
(c) Ze2x
1 + e2xdx =1
2ln(1 + e2x) + C
(Again, why don’t we need the absolute value symbols in the answer?)
(d) Z√2 + ln x
xdx =2
3(2 + ln x)3/2+C
(e) Z3
√6
x√x2
−5dx =7
3
2. The answer to each of the following questions is the value of a definite integral. In
each of these problems, set up the integral that gives the answer to the question, but
DO NOT EVALUATE THE INTEGRAL.
Example: ”What is the area under the curve y=x2on the interval [0,1]?”
ANSWER: area = Z1
0
x2dx
(a) What is the area of the region bounded by the curves y=x2
−1 and y=x+ 1?
ANSWER: area = Z2
−1
x+ 2 −x2dx
(b) A population grows at a rate of R(t) = tetmembers per year. What is the cumu-
lative change in the size of the population over the six-month period beginning
at t= 1?
ANSWER: cumulative change = Z1.5
1
tetdt
