Home
Class 12
MATHS
int(0)^(pi/2) sin 2x tan^(-1) (sin x) dx...

`int_(0)^(pi/2) sin 2x tan^(-1) (sin x) dx`

Text Solution

AI Generated Solution

To solve the integral \( I = \int_{0}^{\frac{\pi}{2}} \sin(2x) \tan^{-1}(\sin x) \, dx \), we will follow these steps: ### Step 1: Rewrite the integral We know that \( \sin(2x) = 2 \sin x \cos x \). Therefore, we can rewrite the integral as: \[ I = \int_{0}^{\frac{\pi}{2}} 2 \sin x \cos x \tan^{-1}(\sin x) \, dx \] ...
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Exercise 7.11|21 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|18 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise (prove That )|9 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(pi//2) sin 2x tan^(-1) (sinx)dx =

Evaluate the definite integrals int_(0)^((pi)/(2))sin2x tan^(-1)(sin x)dx

int_(0)^(pi//2) sin 2 x (tan x) dx=

int_(0)^( pi/2)(sin x)*dx

int_(0)^(pi/2) sin^(-1)(sin x)dx

int_(0)^(pi) [2sin x]dx=

Evaluate: int_(0)^((pi)/(2))2sin x cos x tan^(-1)(sin x)dx

int_(0)^( pi)sin(2*x)dx

int_(0)^(pi//2)sinx sin2x sin3x sin 4x dx=

Prove that : int_(0)^(pi//2) (sin x-cos x)/(1+sin x cos x)dx=0 " (ii) Prove that " : int_(0)^(pi//2) sin 2x. log (tan-x) dx=0