_0^ 2 ( x+| x|) d x= - Vidyadip

MCQ

$\int_0^{2 \pi}(\sin x+|\sin x|) d x=$

A
8
B
4
C
0
D
1

✓

Answer

$\begin{aligned} & \text {(b): } \int_0^{2 \pi}(\sin x+|\sin x|) d x \\
& =\int_0^{\pi / 2}(\sin x+\sin x) d x+\int_{\pi / 2}^\pi(\sin x+\sin x) d x \\
& +\int_\pi^{3 \pi / 2}(\sin x-\sin x) d x+\int_{3 \pi / 2}^{2 \pi}(\sin x-\sin x) d x \\
& =\int_0^\pi 2 \sin x d x=[-2 \cos x]_0^\pi \\ & =-2 \cos \pi-(-2 \cos 0)=2+2=4\end{aligned}$

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