Home
Class 12
MATHS
If int(n)=int(-pi)^(pi)(sin nx)/((1+pi^(...

If `int_(n)=int_(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,……….` then

A

`I_(n)=I_(n+2)`

B

`sum_(m=1)^(10)I_(2m+1)=10 pi`

C

`sum_(m=1)^(10)I_(2m)=0`

D

`I_(n)=I_(n+1)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Promotional Banner

Topper's Solved these Questions

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|64 Videos
  • FUNCTIONS

    VMC MODULES ENGLISH|Exercise JEE Main & Advanced|8 Videos
  • INTEGRAL CALCULUS-1

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|25 Videos

Similar Questions

Explore conceptually related problems

If I_n=int_(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... then which one of the following is not true ?

int_(0)^(pi/2) (sinx)/(1+cos^(2)x)dx

int_(0)^( pi)(dx)/(1+sin x)

int_(0)^(pi//2)sinx sin2x sin3x sin 4x dx=

Evaluate: int_(-pi/2)^(2pi)sin^(-1)(sinx)dx

If I_n = int_0^(pi/2) (sin^2 nx)/(sin^2 x) dx , then

Evaluate int_(0)^(pi)(sin 6x)/(sinx) dx .

If I=int_(-pi)^(pi) (sin^(2))/(1+a^(x))dx, a gt 0 , then I equals

int_(0)^(pi)(x)/(1+sinx)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) :

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Advanced (Archive)
  1. Suppose we define integral using the following formula int(a)^(b)f(x)d...

    Text Solution

    |

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

    Text Solution

    |

  3. If int(n)=int(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,………. then

    Text Solution

    |

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

    Text Solution

    |

  5. Let d/(dx)F(x)=(e^(sinx))/x . x lt0. If int(1)^(4)(2e^(sinx^(2)))/xdx=...

    Text Solution

    |

  6. int(1)^(e^(37))(pisin(pilogx))/(x)dx equals to.

    Text Solution

    |

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

    Text Solution

    |

  8. The value of int2^3(sqrt(x))/(sqrt(5-x)+sqrt(x))dxi s

    Text Solution

    |

  9. The value of overset(3pi//4)underset(pi//4)int (x)/(1+sin x) dx is equ...

    Text Solution

    |

  10. The value of int(-2)^2|1-x^2|dx is

    Text Solution

    |

  11. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

    Text Solution

    |

  12. Match the conditions // expression in Column I with statement in Colum...

    Text Solution

    |

  13. Match List I with List II and select the correct answer using the code...

    Text Solution

    |

  14. Evaluate: 5050(int0 1(1-x^(50))^(100)dx)/(int0 1(1-x^(50))^(101)dx)

    Text Solution

    |

  15. Evaluate: int0^pie^(|cosx|)(2s in(1/2cosx)+3cos(1/2cosx))sinxdxdot

    Text Solution

    |

  16. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|pi/3))dx

    Text Solution

    |

  17. Show that: int0^(pi//2)f(sin2x)sinxdx=sqrt(2)int0^(pi//4)f(cos2x)co...

    Text Solution

    |

  18. int(-pi)^(pi) ( e^(sin x ))/( e^(sinx) + e^(-sinx))dx is equal to

    Text Solution

    |

  19. Prove that int(0)^(1)tan^(-1)(1/(1-x+x^(2)))dx=2int(0)^(1)tan^(-1)xdx....

    Text Solution

    |

  20. Evaluate int(0)^(pi//4) log (1+tan theta)d theta

    Text Solution

    |