Fundamental Theorem of Calculus

Practice Questions

AP Calculus AB › Fundamental Theorem of Calculus

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1

Write the domain of the function.

$f(x)=\frac{(x^{4}-81)^{1/2}}{x-4}$

2

Evaluate the definite integral, $\int_{-1}^{2}(2x^2-x+5)(2x-2)dx$

3

Evaluate the indefinite integral:

$\int_0^{\frac{\pi}{4}} \tan(x)\sec^2(x)dx$

4

Evaluate

$\int_{-1}^{e-2}\frac{1}{x+2}$

5

$\int_{-1}^{\pi}\pi x^2dx=$

6

Find the area of the region given by the following integral.

$\int_{0}^{5}5t^4-3t^2+5e^tdt$

7

Evaluate the definite integral, $\int_{-1}^{2}(2x^2-x+5)(2x-2)dx$

8

Evaluate the integral $\int_0^{\pi/2} \frac{\sin^2(x)}{\sec(x)}dx$

9

Evaluate the integral $\int_0^{\pi/2} \frac{\sin^2(x)}{\sec(x)}dx$

10

$\frac{d}{dx}\int_{0}^{x^2} sin(t)dt=?$

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