Score: /10
MAT 168 Quiz 5
Substitution Rule
Name
Instructions: Show any work necessary to obtain the solution. All work should progress clearly and
logically to a final solution. Clearly state any substitution used.
Problem 1: (2 points) Find the following indefinite integral. Then take the derivative to check your
answer. Zsin−1(x)
√1−x2dx
•u= sin−1x
•du = 1/√1−x2dx
Zsin−1(x)
√1−x2dx =Zu du =u2
2+C=(sin−1(x)x)2
2+C
Checking the answer,
d
dx (sin−1(x))2
2=1
22(sin−1(x)) ·1
√1−x2
Problem 2: (2 points) Find the following definite integral.
Z2
1
xe3x2dx
•u= 3x2
•du = 6x dx
•u(2) = 12, and u(1) = 3
Z2
1
xe3x2dx =1
6Z12
3
eudu =1
6[eu]12
3=e12 −e3
6
Problem 3: (2 points) Determine wheter the function f(x) = x
1+x2is even or odd. Use this information
to calcuate Z5
−5
x
1 + x2dx
Plugging in x=−a, we get
f(−a) = −a
1+(−a)2=−a
1+(a)2=−f(a)
Therefore, f(x) is odd, and so
Z5
−5
x
1 + x2dx = 0
