Math 152 — Calculus II
∫
x(4x −
1. Evaluate
∫
Sample Questions for Test #1
1
) dx.
x3
π/3
2. Evaluate
(5 + sin x) dx.
0
∫
x2 sin(x3 ) dx.
3. Evaluate
∫
1
4. Evaluate
0
∫
5. Evaluate
(x2
x−2
dx.
− 4x + 1)2
√
x x − 1 dx.
6. Let f (x) = x5 + x3 + x + 1.
a) Is f one -to -one? Justify.
b) Find f −1 (1) and f −1 (4).
c) Find (f −1 )′ (1).
7. Find the inverse of the function f (x) =
√
6x + 3 and state its domain.
8. Let f (x) = tan−1 (x2 + 1). Find f ′ (x).
9. Find the derivative of the following function y = sin−1 (x −
10. Evaluate the integrals:
∫ 1/2
1
(a)
dx.
1 + 4x2
0
∫
√
(b)
∫
(c)
x2
dx.
1 − 9x6
x
dx.
81 + 16x4
√
x)