Home
Class 12
MATHS
The value of the integral int0^(1/2)(...

The value of the integral `int_0^(1/2)(1+sqrt(3))/(((x+1)^2(1-x)^6)^(1/4))dx` is ______.

Text Solution

Verified by Experts

The correct Answer is:
2
(2) Let `I=int_(0)^(1//2) (1+sqrt(3))/([(x+1)^(2)(1-x)^(6)]^(1//4))dx`
`rArr I=int_(0)^(1//2)(1+sqrt(3))/((1-x)^(2)[((1-x)/(1+x))^(6)]^(1//4))dx`
Put `(1-x)/(1+x)=trArr(-2dx)/((1+x)^(2))=dt`
when `x=0, t =1,x = (1)/(2),t = (1)/(3)`
`:. I= int_(1)^(1//3)((1+sqrt(3))dt)/(-2(t) ^(6//4))`
`rArr I=(-(1+sqrt(3)))/(2)[(-2)/(sqrt(t))]_(1)^(1//3)`
`rArr I=(1+sqrt(3))(sqrt(3)-1)rArrI=3-1=2`
Promotional Banner

Similar Questions

Explore conceptually related problems

The value of the integral int_-2^(2) |1-x^2|dx is

evaluate the integrals int_(0)^(1)x(1-x)dx

The value of the integral int _0^1 1/(1+x^2)^(3/2) dx is

Choose the correct answer The value of the integral int_(1/3)^(1)((x-x^(3))^(1/3))/(x^(4))dx is

Evaluate the integrals int(dx)/(sqrt(1+x)-sqrt(x))

The value of difinite integral int_(0)^(1) (dx)/(sqrt((x+1)^(3)(3x+1))) equals

The value of the definite integral int_(0)^(1)(1+e^(-x^(2))) dx is

Evaluate the definite integrals int_(0)^(1)(2x+3)/(5x^(2)+1)dx

int_(1/sqrt(3))^(sqrt(3))(dx)/(1+x^(2))

Evaluate the following definite integrals : int_(0)^(1) sqrt((1-x)/(1+x)) dx