Home
Class 12
MATHS
Show that int(0)^(pi//2) log (sin x) dx ...

Show that `int_(0)^(pi//2) log (sin x) dx = - pi/2 log 2`

Text Solution

Verified by Experts

The correct Answer is:
`- pi/2 log 2`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise EXERCISE - 2.1 (VERY SHORT ANSWER QUESTIONS)|26 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise EXERCISE - 2.1 ( SHORT ANSWER QUESTIONS)|13 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Exercise (Level-2)|38 Videos

  • COMPLEX NUMBERS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|93 Videos

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise PRACTICE EXERCISE|64 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

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

Which of the following are false : Statement-I : ( int_(0)^(pi//2) (sqrt(cos x))/(sqrt(cos x + sqrt(sin x)))= pi/2 Statement-II : int_(0)^(pi//2) log(tan x) dx=1 Statement-III: int_(0)^(pi//2) log sin x dx = - pi log 2

int_(0)^(pi//2) x sin^(8) 2x dx=

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

Evaluate int_(0)^(pi/2) x sin x dx .

int_(0)^(2pi) ln (1+Cos x) dx=