Home
Class 12
MATHS
Show that underset(0)overset(pi//2)int (...

Show that `underset(0)overset(pi//2)int (x)/(sinx+cosx)dx=(pi)/(2sqrt(2))log (sqrt(2)+1)` .

A

`(pi)/(2sqrt2)log(sqrt2-1)`

B

`(pi)/(2sqrt2)log(sqrt2+1)`

C

`(pi)/(sqrt2)log(sqrt2+1)`

D

none

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1C|33 Videos
  • DEFINITE INTEGRATION

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1D|32 Videos
  • DEFINITE INTEGRATION

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1A|91 Videos
  • DE MOIVRE'S THEOREM

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 SET-4|3 Videos
  • DIFFERENTIAL EQUATIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise Exercise 2|15 Videos

Similar Questions

Explore conceptually related problems

underset(0)overset(pi//2)(dx)/(4+5cosx)

Show that int_(0)^(pi//2) (x)/(sinx+cosx)dx=(pi)/(2sqrt(2))log (sqrt(2)+1) .

int_(0)^(pi//2)(4sinx+3cosx)/(sinx+cosx)dx=

int_(0)^(pi//2)(1)/(2+3sinx)dx=

int_(0)^(pi)(1)/(3+2sinx+cosx)dx=

int_(0)^(pi//2)(cosx)/(1+sinx)dx=

int_(0)^(pi//2)(200sinx+100cosx)/(sinx+cosx)dx=

int (sinx+cosx)/(sqrt(1+sin 2x))dx=

Prove that int_(0)^(pi//2)(cos^(2) x sin x)/(sqrt(1+cos^(2)x))dx = (sqrt(2) - log(sqrt(2) + 1))/2