Home
Class 12
MATHS
Let I(n)=int(0)^(pi//2) sin^(n)x dx, nin...

Let `I_(n)=int_(0)^(pi//2) sin^(n)x dx, nin N`. Then

A

`I_(n):I_(n-2)=n:(n-1)`

B

`I_(n) gt I_(n-2)`

C

`n(I_(n-2)-I_(n))=I_(n-2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Chapter Test 2|60 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Exercise|147 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA|Exercise Exercise|86 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

Let I_(n)=int_(0)^(pi//4)tan^(n)xdx,n in N , Then

If l_(n)=int_(0)^(pi//4) tan^(n)x dx, n in N "then" I_(n+2)+I_(n) equals

Let f(x) = int_(0)^(pi)(sinx)^(n) dx, n in N then

let I_(n)=int_(0)^((pi)/(4))tan^(n)xdx,n>1

Let I_(n)=int_(0)^(pi//2)(sinx+cosx)^(n)dx(nge2) . Then the value of n. I_(n)-2(n-1)I_(n-1) is

I_(n)=int_(0)^(pi//4) tan^(n)x dx , where n in N Statement-1: int_(0)^(pi//4) tan^(4)x dx=(3pi-8)/(12) Statement-2: I_(n)+I_(n-2)=(1)/(n-1)

Let I_(n)=int_(0)^(pi//2)x^(n)cosxdx, where in is a non-negative integer Then sum_(n=2)^(oo)((I_(n))/(n!)+(I_(n-2))/((n-2)!)) equals-

If I_(n)=int_(0)^(pi/2) sin^(x)x dx , then show that I_(n)=((n-1)n)I_(n-2) . Hence prove that I_(n)={(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(1/2)(pi)/2,"if",n"is even"),(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(2/3)1,"if",n"is odd"):}

If u _(n) = int _(0) ^(pi//2) x ^(n) sin x dx, n in N then the value of u _(10) + 90 u _(s) is

OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 1
  1. |int(10)^(19) (sin x)/(1+x^(8))dx| is less than

    Text Solution

    |

  2. The smallest interval [a,b] such that int0^(1) (1)/(sqrt(1+x^(4)))dx...

    Text Solution

    |

  3. Let I(n)=int(0)^(pi//2) sin^(n)x dx, nin N. Then

    Text Solution

    |

  4. If f(x)=int(0)^(x) sin^(4)t dt, then f(x+2pi) is equal to

    Text Solution

    |

  5. int(0)^(pi) (1)/(1+3^(cosx)) dx is equal to

    Text Solution

    |

  6. Let int(0)^(a) f(x)dx=lambda and int(0)^(a) f(2a-x)dx=mu. Then, int(...

    Text Solution

    |

  7. The value of int(pi//4)^(3pi//4) (x)/(1+sin x) dx is equal to

    Text Solution

    |

  8. Let I(n)=int(0)^(pi//2) cos^(n)x cos nx dx. Then, I(n):I(n+1) is equal...

    Text Solution

    |

  9. The value of int(-1)^(1) max[2-x,2,1+x] dx is

    Text Solution

    |

  10. int(0)^(pi//4) sin(x-[x]) dx is equalto

    Text Solution

    |

  11. The value of the integral int(-1)^(1) (x-[2x])dx,is

    Text Solution

    |

  12. Let f:R in R be a continuous function such that f(1)=2. If lim(x to 1)...

    Text Solution

    |

  13. Let f:R in R be a continuous function such that f(x) is not identicall...

    Text Solution

    |

  14. Let f(x)=int(0)^(x) |xx-2|dx, ge 0. Then, f'(x) is

    Text Solution

    |

  15. Lt(nrarroo) {(n!)/(kn)^n}^(1/n), k!=0, is equal to (A) k/e (B) e/k (C)...

    Text Solution

    |

  16. Let f(x) be an integrable function defined on [a,b],b gt a gt 0. If I(...

    Text Solution

    |

  17. int(0)^(sqrt(2)) [x^(2)]dx, is

    Text Solution

    |

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

    Text Solution

    |

  19. (sum(n=1)^10int(-2n-1)^(-2n)sin^(27)(x)dx+sum(n=1)^10int(2n)^(2n+1)sin...

    Text Solution

    |

  20. If f(y)=e^(y)=e^(y),g(y)=y, y gt 0 and F(t)=int(0)^(t) f(t-y)g(y) dy, ...

    Text Solution

    |