1)

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


A) 0

B) 4

C) 8

D) 1

Answer:

Option B

Explanation:

$  \int_{0}^{2x} (\sin x+|\sin x|)dx$

= $  \int_{0}^{\pi} (\sin x+\sin x)dx$+$  \int_{\pi}^{2 \pi} (\sin x-\sin x)dx$

  =$ 2\int_{0}^{\pi} \sin x dx$+0=$ 2 \int_{0}^{\pi} \cos x dx$

 =    $-2(\cos \pi-\cos 0)=-2(-1-1)=4$