First slide

Evaluation of definite integrals

Question

$\int_{0}^{2 π} (\sin x + | \sin x |) dx$ is equal to

Moderate

A

0
B

4
C

8
D

1

Solution

$\begin{array}{l} \int_{0}^{2 π} (\sin x + | \sin x |) dx \\ = \int_{0}^{π} (\sin x + \sin x) dx + \int_{π}^{2 π} (\sin x - \sin x) dx \\ = \int_{0}^{π} 2 \sin xdx + \int_{π}^{2 π} 0 dx = 2 [- \cos x]_{0}^{π} + 0 \\ = - 2 (\cos π - \cos 0) = - 2 (- 1 - 1) = 4 \end{array}$

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