Home
Class 12
MATHS
if int0^(pi)(x/(1+sinx))^2dx=A, then int...

if `int_0^(pi)(x/(1+sinx))^2dx=A`, then `int_0^(pi)((2x^2).(cos^2(x/2)))/(1+sinx)^2` is equal to

A

`A+2pi-pi^2`

B

`A-2pi+pi^2`

C

`2pi-A-pi^2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY & DIFFERENTIABILITY

    PATHFINDER|Exercise QUESTION BANK|13 Videos
  • DETERMINATES

    PATHFINDER|Exercise QUESTION BANK|21 Videos

Similar Questions

Explore conceptually related problems

int_0^pi (xdx)/(1+sinx) is equal to

int_(0)^((pi)/(2))(cosxdx)/(1+sinx)

Evaluate int_0^(pi/2)(cosx)/(1+sinx)^2dx

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

Evaluate: int_0^pi(dx)/(1+sinx)

The value of int_(0)^(pi)(|x|sin^(2)x)/(1+2|cosx|sinx)dx is equal to

Evaluate: int_0^(pi//2)1/((a^2cos^2x+b^2sin^2x)^2)dx

Evaluate: int_0^(pi/4)(sinx+cosx)/(9+16sin2x)dx

The value of int_(0)^(pi) (x)/(a^(2)cos^(2)x+b^(2)sin^(2)x)dx is equal to -

Evalute: int_0^(pi)(xsinx)/(1+cos^2x)dx .

PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. ifint0^1 f(x)dx=1,int0^1 xf(x)dx=a and int0^1 x^2f(x)dx=a^2 ,then int0...

    Text Solution

    |

  2. if f(x)=-int0^xlog(cost)dt, then the value of f(x)-2f(pi/4+x/2)+2f(pi/...

    Text Solution

    |

  3. if int0^(pi)(x/(1+sinx))^2dx=A, then int0^(pi)((2x^2).(cos^2(x/2)))/(1...

    Text Solution

    |

  4. If intsin^4x/(cos^8x)dx= atan^7x+btan^5x+c then find the relation betw...

    Text Solution

    |

  5. The value of x satisfying int0^(2[x+14]){x/2}dx=int0^({x})[x+14]dxis e...

    Text Solution

    |

  6. if ngt1and I=int0^infty dx/((x+sqrt(1+x^2))^n then I equals

    Text Solution

    |

  7. If [x] denotes the greatest integer lex and n inN then value of In=int...

    Text Solution

    |

  8. if I=int0^1dx/((1+x)(2+x)sqrtx(1-x)then I equals

    Text Solution

    |

  9. if int0^1 x(1-x)^(2007//2)dx then it equals

    Text Solution

    |

  10. if I=int(-1)^2abs(xsinpix)dx then I equals

    Text Solution

    |

  11. if I=int(alpha)^(beta)[loglogx+1/(logx)^2]dx then I equals

    Text Solution

    |

  12. if I=int0^(pi/4) (sin2theta)/(sin^2theta+cos^4theta)d(theta) then I eq...

    Text Solution

    |

  13. if 0ltalphalt1 and I=int(-1)^1dx/(sqrt(1-2alphax+alpha^2) then I equal...

    Text Solution

    |

  14. if I=int8^15 dx/((x-3)sqrt(x+1)) then I equals

    Text Solution

    |

  15. underset(xrarr(pi//4))lim( int2^(sec^2x)(f(t)dt))/(x^2-(pi)^2/16 equal...

    Text Solution

    |

  16. If int1^infty((x^3+3)dx)/(x^6(x^2+1))=(a+bpi)/c, then

    Text Solution

    |

  17. If int0^1 ((1-x^2)dx)/(1+x^2+x^4) =aInb then,

    Text Solution

    |

  18. If f(x)=int(-2)^xabs(t+1)dt then,

    Text Solution

    |

  19. Let f(x)be a function satisfying f(x)=f(x) with f(0)=1 and 'g' be the ...

    Text Solution

    |

  20. Let In=int0^(pi/4)tan^nxdx, then 1/(I2+I4),1/(I3+I5), 1/(I4+I6), 1/(I5...

    Text Solution

    |