Home
Class 12
MATHS
Prove that: int0^(2pi)(xsin^(2n)x)/(...

Prove that: `int_0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx`= `pi^2`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    RD SHARMA ENGLISH|Exercise All Questions|282 Videos

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA ENGLISH|Exercise All Questions|168 Videos

Similar Questions

Explore conceptually related problems

For n gt 0 int_(0)^(2pi)(x sin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx= ….

Evaluate int_(0)^(2pi)(xcos^(2n)x)/(cos^(2n)x+sin^(2n)x)dx

Prove that : int_(0)^(pi//2) (cos^(5))/(sin^(5) x+cos^(5) x)dx= (pi)/(4)

int_0^(pi//4)(x^2(sin2x-cos2x))/((1+sin2x)cos^2x)dx

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

int_(0)^(pi/2) (cos^(2)x dx)/(cos^(2)x+4 sin^(2)x)

Prove that : int_(0)^(pi) (x sin x)/(1+cos^(2)x) dx =(pi^(2))/(4)

Prove that : int_(0)^(pi) (x)/(a^(2) cos^(2) x+b^(2) sin^(2) x)dx =(pi^(2))/(2ab)

Evaluate: int_0^(pi/2) (sin2x)/(sin^4x+cos^4x)dx

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

RD SHARMA ENGLISH-DEFINITE INTEGRALS-All Questions
  1. For x >0,l e tf(x)=int1^x((log)e t)/(1+t)dtdot Find the function...

    Text Solution

    |

  2. Evaluate the following integrals: (1-35) int0^(pi//2)(sin^n x)/(sin...

    Text Solution

    |

  3. Prove that: int0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx= pi^2

    Text Solution

    |

  4. Prove that: int0^(pi//2)log|tanx+cotx|dx=pi(log)e2

    Text Solution

    |

  5. Evaluate: int(-2)^2|xcospix|dx

    Text Solution

    |

  6. Evaluate: int(-pi//2)^(pi//2)log(sinx+cosx)dx

    Text Solution

    |

  7. Evaluate: int0^pixlogsinxdx

    Text Solution

    |

  8. If int0^pi 1/(a+bcosx)dx=pi/sqrt(a^2-b^2), then int0^pi 1/(a+bcosx)^2d...

    Text Solution

    |

  9. int0^1sqrt((1-x)/(1+x))dx= (a) (pi)/2 (b) (pi)/2-1 (c) (pi)/2+1 (d...

    Text Solution

    |

  10. int0^(pi//2)(cosx)/((2+sinx)(1+sinx))dx equals (a)log(2/3) (b) l...

    Text Solution

    |

  11. int0^pi(xtanx)/(secx+cosx)dxi s (a) (pi^2)/4 (b) (pi^2)/2 (c) (3pi^2...

    Text Solution

    |

  12. int0^21/(1+tanx)dx is equal to (pi^)/4 (b) (pi^)/3 (c) (pi^)/...

    Text Solution

    |

  13. int(-pi//2)^(pi//2)"sin"|x|dx is equal to (a) 1 (b) 2 (c) -1 (d)...

    Text Solution

    |

  14. The value of the integral int0^oox/((1+x)(1+x^2))dx is (pi^)/2 (b) ...

    Text Solution

    |

  15. int0^3(3x+1)/(x^2+9)dx = (pi^)/(12)+log(2sqrt(2)) (b) (pi^)/2+log(2...

    Text Solution

    |

  16. I10=int0^(pi/2)x^(10)sinx dx then I10+90I8 is (A) 10(pi/2)^6 (B) 10(p...

    Text Solution

    |

  17. The derivative of f(x)=int(x^2)^(x^3)1/((log)e t)dt ,(x >0), is 1/(...

    Text Solution

    |

  18. Evaluate:int0^(pi//2)(cosx)/(1+cosx+sinx)dx

    Text Solution

    |

  19. Evaluate: int0^(pi//2)1/(3+2cosx)dx

    Text Solution

    |

  20. Evaluate: int(pi//4)^(pi//2)cos2xlogsinxdx

    Text Solution

    |