M408C
11/21/2013
Worksheet: Inverse Trig Integrals
We’re a little behind Professor Davis’s lectures. Here’s the plan for the rest of the semester:
11/21 - Inverse Trig, 11/26 - Trig Substitution, 12/3 - Partial Fractions, 12/5 - Final Review
Things are starting to go very fast and we won’t be able to cover everything. Study, study, study!
Quick Recap:
Below is the domain and range of a few inverse trig functions:
sin−1(x) : domain = [−1,1],range = h−
π
2,π
2i
tan−1(x) : domain = (−∞,∞),range = h−
π
2,π
2i
Here are a few useful freeby integrals for any a > 0:
Z1
√a2−x2dx = sin−1x
a+C, Z1
a2+x2dx =1
atan−1x
a+C.
Examples:
(1) Z1
0
1
√4−x2dx
(2) Zx2
x2−x+ 1 dx
Answers: (1) π
6,(2) x+1
2ln |x2−x+ 1| − 1
√3tan−12x−1
√3+C
1
