1. Find the following indefinite integrals:
| a. | ∫ x2 dx | b. | ∫ 2x dx | c. | ∫ 4 dx |
| d. | ∫ x dx | e. | ∫ 3x2 dx | f. | ∫ 5x4 dx |
| g. | ∫ -2x dx | h. | ∫ 0.75x4 dx | i. | ∫ (x2 − 2x − 3) dx |
| j. | ∫ (4x3 − 3x2 + 2x − 6) dx | k. | ∫ (x6 − x5 − x4) dx | l. | ∫ 3(x − 2) dx |
| m. | ∫ -2(x2 − 4) dx | n. | ∫ (2x + 1)(x − 6) dx | o. | ∫ (x − 1)2 dx |
| p. | ∫ 3x(x2 − 4) dx | q. | ∫ (3 − x)(x + 6) dx | r. | ∫ 2(x − 1)3 dx |
2.Anti-differentiate the following derived functions
a. f '(x) = x2 − 3x + 4
b. g'(x) = 2x − 3
c. y ' = 4x3 − 3x2 + 5
d.
= x2 − 4
e.
3. Integrate to find the original function for each of the following derived functions:
| Derived function | Conditions | |
| a. | f '(x) = 3x2 | f(2) = 5 |
| b. | g '(x) = x2 + 4x | g(0) = 4 |
| c. | h '(x) = x2 + 2x − 15 | h(3) = -5 |
| d. | = 6x2 − 5x − 25 |
y= 0 when x = -2 |
| e. | = (x − 2)2 |
y = 1 when x = 2 |
