Home
Class 12
MATHS
Evaluate: int0^(pi//2)(sqrt(s in x))/(sq...

Evaluate: `int_0^(pi//2)(sqrt(s in x))/(sqrt(s in x)+sqrt(cos x))dx`

Text Solution

AI Generated Solution

To evaluate the integral \[ I = \int_0^{\frac{\pi}{2}} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx, \] we can use a property of definite integrals. This property states that: ...
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    RD SHARMA|Exercise Solved Examples And Exercises|277 Videos
  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

int_(0)^((pi)/(2))(sqrt(sin x))/(sqrt(sin x)+sqrt(cos x))dx

int_(0)^(pi//2) sqrt(sin x)/(sqrt(sin x ) + sqrt( cos x)) dx =

The value of int_(0)^( pi/2)(sqrt(cos x))/(sqrt(sin x)+sqrt(cos x))dx

By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(2))(sqrt(sin x))/(sqrt(sin x)+sqrt(cos x))dx

Prove that : int_(0)^(pi//2) (sqrt(cos x))/(sqrt(sin x+ sqrt(cos x)))dx=(pi)/(4)

int_(0)^(pi//2)((pi)/(4)-x)/(sqrt(sin x)+ sqrt(cos x))dx=

int_(0)^((pi)/(2))(sqrt(cot x))/(sqrt(tan x)+sqrt(cot x))dx=

int_(0)^((pi)/(2))(sqrt(tan x))/(sqrt(tan x+sqrt(cot x)))dx

The value of int_0^(pi//2)(sqrt(cosx))/(sqrt(cos x)+sqrt(s in x))dx is pi//2 b. pi//4 c. 0 d. none of these