Math 105
Integration Questions from recent finals
Richard Anstee 2016
This list may grow over time. For the stated definite or indefinite integrals determne the answer.
1. Given f 0 (1) = 2 and f 0 (2) = 3, determine
Z 2
f 0 (x)f 00 (x)dx
1
2.
3.
Z
Z
cos−1 (x)dx
cos3 (x) sin4 (x)dx
4.
Z
√
5.
dx
3 − 2x − x2
x − 13
dx
−x−6
Z
x2
6. Determine k so that
Z 1
(1 + k|x|)dx = 1
−1
7.
Z 5/2
dx
√
25 − x2
0
8.
Z 2
|2x| dx
−1
9. Compute F 0 (π) given
F (x) =
Z cos(x)
0
t3
1
dt
+6
10. Compute the area bounded by the curve y = f (x) and the x-axis and between x = 0 and
x = 1.
1
f (x) =
(2x − 4)2
11.
Z
ln(x)
dx
x7
12. (this was a 6 mark question). You are given f (0) = 1, f (2) = 3, and f 0 (2) = 4. Determine
Z 4
0
√
f 00 ( x)dx