Solveeit Logo
Login

Question

Question: \(\int_{- \pi/2}^{\pi/2}\sqrt{\frac{1 - \cos 2x}{2}}\)dx equals:...

∫−π/2π/21−cos⁡2x2\int_{- \pi/2}^{\pi/2}\sqrt{\frac{1 - \cos 2x}{2}}dx equals:

A

1

B

2

C

½

D

0

Answer

2

Explanation

Solution

I = ∫−π/2π/2∣sin⁡x∣dx\int_{- \pi/2}^{\pi/2}{|\sin x|dx}= 2∫0π/2∣sin⁡x∣dx\int_{0}^{\pi/2}{|\sin x|dx} (Even function)

= 2 ∫0π/2sin⁡x=−2[cos⁡x]0π/2\int _ { 0 } ^ { \pi / 2 } \sin x = - 2 [ \cos x ] _ { 0 } ^ { \pi / 2 }= 2