Home
Class 12
MATHS
If Un=int0^pi(1-cosnx)/(1-cosx)dx , wher...

If `U_n=int_0^pi(1-cosnx)/(1-cosx)dx ,` where `n` is positive integer or zero, then show that `U_(n+2)+U_n=2U_(n+1)dot` Hence, deduce that `int_0^(pi/2)(sin^2ntheta)/(sin^2theta)=1/2npidot`

Text Solution

Verified by Experts

The correct Answer is:
`=(1)/(2)n pi`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 1|15 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 2|14 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

If U_(n)=int_(0)^( pi)(1-cos nx)/(1-cos x)dx, where n is positive integer or zero,then show that U_(n+2)+U_(n)=2U_(n+1). Hence,deduce that int_(0)^((pi)/(2))(sin^(2)n theta)/(sin^(2)theta)=(1)/(2)n pi

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

Show that int_(0)^(n pi+v)|sin x|dx=2n+1-cos v, where n is a positive integer and ,0<=v

int_(-pi//2)^(pi//2)(sin^(2n-1)x)/(1+cos^(2n)x)dx=

The value of I(n)=int_(0)^( pi)(sin^(2)n theta)/(sin^(2)theta)d theta is (AA n in N)

If U_n=int_0^(pi/2)(sin^2n x)/(sin^2x)dx, then show that U_1,U_2,U_3.......U_n constitute an AP. Hence or otherwise find the value of U_n.

If n is a positive integer, prove that: int_0^(2pi) (cos(n-1)x-cosnx)/(1-cosx)dx=2pi , hence or otherwise, show that int_0^(2pi) (sin((nx)/2)/sin(x/2))^2dx=2npi .

If n is a positive integer and u_(n)=int x^(n)sqrt(a^(2)-x^(2))dx

If I _(n)=int _(0)^(pi) (sin (2nx))/(sin 2x)dx, then the value of I _( n +(1)/(2)) is equal to (n in I) :

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If Un=int0^pi(1-cosnx)/(1-cosx)dx , where n is positive integer or zer...

    Text Solution

    |

  2. The value of int(-pi//2)^(pi//2) (x^(2)cos x )/(1+e^(x)) dx is equal ...

    Text Solution

    |

  3. The total number for distinct x epsilon[0,1] for which int(0)^(x)(t^(2...

    Text Solution

    |

  4. Let f(x)=7 tan^(8) x +7 tan^(6) x-3 tan^(4) x-3 tan^(2)x for all x in...

    Text Solution

    |

  5. Let f prime(x)=(192x^3)/(2+sin^4 pix) for all x in RR with f(1/2)=0. I...

    Text Solution

    |

  6. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  7. Let F:R- R be a thrice differentiable function. Suppose that F(1)=0,F(...

    Text Solution

    |

  8. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  9. Let f: RvecR be a function defined by f(x)={[x],xlt=2 0,x >2 where [...

    Text Solution

    |

  10. If alpha=int0^1(e^9x+3tan^((-1)x))((12+9x^2)/(1+x^2))dxw h e r etan^(-...

    Text Solution

    |

  11. The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equ...

    Text Solution

    |

  12. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  13. Match the conditions/ expressions in Column I with statement in Column...

    Text Solution

    |

  14. Match List I with List II and select the correct answer using codes gi...

    Text Solution

    |

  15. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dxi s

    Text Solution

    |

  16. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

    Text Solution

    |

  17. The value of int(sqrt(ln2))^(sqrt(ln3)) (xsinx^2)/(sinx^2+sin(ln6-x^2)...

    Text Solution

    |

  18. Let f:[1,oo] be a differentiable function such that f(1)=2. If int1...

    Text Solution

    |

  19. The value of int(0)^(1) (x^(4)(1-x)^(4))/(1+x^(2)) dx is (are)

    Text Solution

    |

  20. For a in R ( the set of all real number) , a ne -1, lim(n to oo)((1^...

    Text Solution

    |

  21. Consider the statements : P : There exists some x IR such that f(x)...

    Text Solution

    |