Question

$\int _ { 0 } ^ { \pi / 2 } \frac { \sqrt { \tan x } } { 1 + \sqrt { \tan x } } = \int _ { 0 } ^ { \pi / 2 } \frac { \sqrt { \sin x } } { \sqrt { \sin x } + \sqrt { \cos x } } d x$ is equal to

• A. π/4
• B. ∞
• C. –1
• D. 1

Answer 1

Answer: (A)

π/4

Answer 2

We know, $\int _ { 0 } ^ { \pi / 2 } \frac { \tan ^ { n } x d x } { 1 + \tan ^ { n } x } = \frac { \pi } { 4 }$ for any value of n

∴ $I = \pi / 4$.

(5) $\int _ { - a } ^ { a } f ( x ) d x = \int _ { 0 } ^ { a } f ( x ) + f ( - x ) d x$.

In special case : This property is generally used when integrand is either even or odd function of x.