Home
Class 12
MATHS
int (-pi/2)^(pi/2)log((2-sin x)/(2+sinx)...

` int _(-pi/2)^(pi/2)log((2-sin x)/(2+sinx))dx ` is equal to

A

1

B

3

C

2

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
We have, `l=int_((-pi)/(2))^((pi)/(2))log((2-sin x)/(2+sin x))dx`
Let `f(x)=log((2-sin x)/(2+sin x))`
Then, `f(-x)=log((2-sin(-x))/(2+sin(-x)))`
`=log((2+sin x)/(2-sin x))=log((2-sin x)/(2+sin x))^(-1)`
`=-log((2-sin x)/(2+sin x))=-f(x)`
Then, f(x) is an odd function.
`therefore int_(-(pi)/(2))^((pi)/(2))f(x)dx=0`
[`because` If f(x) is an odd function, then `int_(-a)^(a)f(x)dx=0`]
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)|76 Videos

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|16 Videos

  • DIFFERENTIAL EQUATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|27 Videos

Similar Questions

Explore conceptually related problems

int _(-pi //2) ^(pi//2) log ((2-sin x)/(2+sin x))dx=

int_(-pi/4)^(pi/4) log((2 - sinx)/(2 + sinx)) dx=

int_(-(pi)/(2))^((pi)/(2))log((2-sin x)/(2+sin x))dx

Evaluate int_(-pi/2)^(pi/2) log((2-sinx)/(2+sinx))dx

Evaluate the following : int_(-pi//2)^(pi//2)log((2-sinx)/(2+sinx))dx

Evaluate the following integral: int_(-pi//2)^(pi//2)log((2-sinx)/(2+sinx))dx

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

The value of the integral int_(pi//6)^(pi//2)((sinx-xcosx))/(x(x+sinx))dx is equal to

((int (x)/(2))/(-(x)/(2)))log((2-sinx)/(2+sin x)) dx is equal to

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