Home
Class 12
MATHS
Evaluate: int0^1sin^(-1)((2x)/(1+x^2))dx...

Evaluate: `int_0^1sin^(-1)((2x)/(1+x^2))dx`

Text Solution

Verified by Experts

`I=int_0^1sin^(-1)((2x)/(1+x^2))dx`
Also, let `x=tan(theta)=>dx=sec^2thetad theta `
when `x=0, theta=0` and when `x=1,theta=pi/4`
`:. I= int_0^(pi/4)sin^(-1)((2tantheta)/(1+tan^2theta))sec^2thetad theta`
...
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.7|14 Videos

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.5|23 Videos

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.6|24 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT|Exercise EXERCISE 9.1|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT|Exercise MISCELLANEOUS EXERCISE|17 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int sin^(-1)((2x)/(1+x^(2)))dx

int_0^1sin^(-1)(x)/sqrt(1-x^2) dx

Evaluate: int(sin^(-1)x)^(2)dx

Evaluate: int(sin(tan^(-1)x))/(1+x^(2))dx

Evaluate: int(sin^-1x)^2dx

Evaluate the following integral: int_0^1tan^(-1)\ ((2x)/(1-x^2))dx

Evaluate the following integral: int_0^1tan^(-1)((2x)/(1-x^2))dx

Evaluate: int_0^(1/2) (sin^-1x)/(1-x^2)^(3/2)dx

Evaluate: inte^(sin^-1x)/sqrt (1-x^2)dx