AP Calculus AB - Integration - 7 Questions

1. What is the antiderivative of 2x?

a) x^2 + C

(b) 2x + C

c) x/2 + C

d) 4x + C

2. Evaluate the definite integral ∫(3x^2 + 2) dx over the interval [1, 3].

a) 24

(b) 26

(c) 28

Answer: (d) 30
Explanation: To evaluate the definite integral, we need to find the antiderivative of the integrand and evaluate it at the upper and lower limits. The antiderivative of (3x^2 + 2) is x^3 + 2x. Evaluating the antiderivative at 3 and 1 and subtracting the values, we get (3^3 + 2(3)) – (1^3 + 2(1)) = 27 + 6 – 1 – 2 = 30.

(d) 30

3. Find the area bounded by the curve y = 2x and the x-axis over the interval [0, 4].

(a) 4

(b) 8

(c) 12

(d) 16

4. Evaluate the definite integral ∫(5) dx over the interval [0, 2].

(a) 0

(b) 2

(c) 5

(d) 10

5. Find the area bounded by the curves y = x^2 and y = 2x^2 over the interval [0, 2].

a) 2

(b) 4

(c) 6

(d) 8

6. What is the antiderivative of e^x?

(a) e^x + C

(b) ln(x) + C

c) 1/x + C

(d) cos(x) + C

7. Evaluate the definite integral ∫(4sin(x)) dx(a) -4cos(x)

(a) -4cos(x)

(b) 4cos(x)

(c) -4sin(x)

d) 4sin(x)