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Question: The value of the integral <img src="https://cdn.pureessence.tech/canvas_113.png?top_left_x=300&top_l...

The value of the integral dx is

A

π3\frac { \pi } { 3 }

B

π6\frac { \pi } { 6 }

C

π12\frac { \pi } { 12 }

D

0

Answer

π12\frac { \pi } { 12 }

Explanation

Solution

∫π/6π/3dx1+sin⁡xcos⁡x\int _ { \pi / 6 } ^ { \pi / 3 } \frac { d x } { 1 + \sqrt { \frac { \sin x } { \cos x } } } = ∫π/6π/3cos⁡xcos⁡x+sin⁡x\int _ { \pi / 6 } ^ { \pi / 3 } \frac { \sqrt { \cos x } } { \sqrt { \cos x } + \sqrt { \sin x } } dx

= π3−π62\frac { \frac { \pi } { 3 } - \frac { \pi } { 6 } } { 2 } = π12\frac { \pi } { 12 }