Home
Class 12
MATHS
int(0)^(pi//2)(sqrt(cotx))/((1+sqrt(cotx...

`int_(0)^(pi//2)(sqrt(cotx))/((1+sqrt(cotx)))dx=?`

A

`(pi)/(4)`

B

`(pi)/(2)`

C

`0`

D

`1`

Text Solution

AI Generated Solution

To solve the integral \( I = \int_{0}^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{1 + \sqrt{\cot x}} \, dx \), we can follow these steps: ### Step 1: Rewrite the Integral Start with the given integral: \[ I = \int_{0}^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{1 + \sqrt{\cot x}} \, dx \] ...
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    RS AGGARWAL|Exercise Exercise 16D|17 Videos

  • CROSS,OR VECTOR, PRODUCT OF VECTORS

    RS AGGARWAL|Exercise Exercise 24|26 Videos

  • DETERMINANTS

    RS AGGARWAL|Exercise Objective Questions|29 Videos

Similar Questions

Explore conceptually related problems

sqrt(1+cotx)

int_(0)^(pi//2)(sqrt(tanx)+sqrt(cotx))\ dx

The value of the integral int_(0)^(pi//2)(sqrt(cotx))/(sqrt(cotx)+sqrt(tanx))dx is

int_(0)^(pi//4)(sqrt(tanx)+sqrt(cotx))dx equals

Evaluate the following integral: int_0^(pi//2)(sqrt(cotx))/(sqrt(cotx\ )+sqrt(tanx))dx

Prove that : int_(0)^(pi//2) (sqrt(tanx))/(sqrt(tanx +sqrt(cotx)))dx=(pi)/(4)

Evaluate the following : int_(0)^(pi//2)(sqrt(tanx))/(sqrt(tanx)+sqrt(cotx))dx

(2cotx)/(sqrt(x))

int_(0)^(pi//2)(1)/((1+sqrt(cotx)))dx=?