Use of the Fundamental Theorem to evaluate definite integrals

Practice Questions

AP Calculus AB › Use of the Fundamental Theorem to evaluate definite integrals

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1

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

2

Using the Fundamental Theorem of Calculus and simplify completely solve the integral.

$\int_{3}^{6}\frac{dx}{x}$

3

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

4

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

5

Evaluate the indefinite integral:

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

6

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

7

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

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

8

Evaluate

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

9

Evaluate $\int_{0}^{3}(6x^2+1)\mathrm{d}x$

10

Use the fundamental theorem of Calculus to evaluate the definite integral

$\int_{\pi/2}^{\pi}(2cos(x)+1)dx$

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