Home
Class 12
MATHS
The value of int (0)^(pi//2) log ("cosec...

The value of `int _(0)^(pi//2) log ("cosec "x) dx` is

A

`pi/2 log 2`

B

`pi log 2`

C

` -pi/2log2`

D

`2pi log2`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `l = int_(0)^(pi//2) log ("cosec " x) dx`
`= int_(0)^(pi//2) log((1)/(sin x))dx = - int_(0)^(pi//2)` log sin x dx
`= (pi)/(2)log 2 " " [ because int_(0)^(pi//2)" log sin x dx" = -(pi)/(2) log 2]`
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_(0)^(pi//2)log (sec x) dx=

The value of int_(0)^(pi//2) log (sinx) dx is

int_(0)^(pi//2) log (cotx ) dx=

What is the value of int_(0)^(pi/2) log (tanx) dx ?

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

The value of int_(0)^(pi//2) (2log sin x-log sin 2x)dx , is

The value of int_(0)^(pi//2) (sin 8x log cot x)/(cos 2x)dx , is