Home
Class 12
MATHS
If In=int-pi^pi (sinnx)/((1+pi^x)sinx)dx...

If `I_n=int_-pi^pi (sinnx)/((1+pi^x)sinx)dx, n=0,1,2, …,` then (A) `I_n=I_(n+2)` (B) `sum_(m=1)^10 I_(2m+1)=10pi` (C) `sum_(m=1)^10 I_(2m)=0` (D) `I_n=I_(n+1)`

A

0

B

`5pi`

C

`10pi`

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 5|20 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 6|10 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 3|20 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 I_(n)=int_(0)^(pi)(1-sin2nx)/(1-cos2x)dx then I_(1),I_(2),I_(3),"….." are in

If I_n=int_(pi/4)^(pi/2) (tanx)^-n dx(ngt1) , then I_n+I_(n+2)= (A) 1/(n-1) (B) 1/(n+1) (C) -1/(n+1) (D) 1/n-1

If I_(n)=int_(0)^( pi)e^(x)(sin x)^(n)dx, then (I_(3))/(I_(1)) is equal to

If I_(n)=int_(0)^(pi//4)tan^(n)x dx , where n ge 2 , then : I_(n-2)+I_(n)=

If I(m,n)=int_(0)^(1)x^(m-1)(1-x)^(n-1)dx, then

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) :

If sum_(r=1)^(n)I(r)=2^(n)-1 then sum_(r=1)^(n)(1)/(I_(r)) is

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise For Session 4
  1. Let f : R -> R and g : R -> R be continuous functions. Then the value...

    Text Solution

    |

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

    Text Solution

    |

  3. The value of int(-1)^(1)((x^(2)+ sin x)/(1+x^(2)))dx is equal to

    Text Solution

    |

  4. If f(x) is an odd function, then the value of int(-a)^(a)(f(sin x)/(f(...

    Text Solution

    |

  5. Evaluate: int-(1/sqrt(3))^(1/sqrt(3)) (cos^-1((2x)/(1+x^2))+tan^-1((2x...

    Text Solution

    |

  6. The value of int(-pi)^(pi)(cos^(2)x)/(1+a^(x)dx where agt 0, is

    Text Solution

    |

  7. The integral int(-1/2)^(1/2) ([x]+1n((1+x)/(1-x)))dx is equal to (wher...

    Text Solution

    |

  8. The value of int(-pi//2)^(pi//2)(1)/(e^(sinx)+1) dx is equal to

    Text Solution

    |

  9. If [*] denots the greatest integer function then the value of the inte...

    Text Solution

    |

  10. The equation int(-pi/4)^(pi/4){a|sinx|+(bsinx)/(1+cos^2x)+c}dx=0 where...

    Text Solution

    |

  11. The value of int(-2)^(2)(sin^(2)x)/([(x)/(pi)]+(1)/(2))dx where [.] d...

    Text Solution

    |

  12. Let f(x) be a contiuous function such a intn^(n+1) f(x)dx=n^3, n in Z...

    Text Solution

    |

  13. Let f(x)=(e^(x)+1)/(e^(x)-1) and int(0)^(1) x^(3) .(e^(x)+1)/(e^(x)-1)...

    Text Solution

    |

  14. Let f: R rarr R be a continuous function given by f(x+y)=f(x)+f(y) for...

    Text Solution

    |

  15. The value of int(-2)^(2) |[x]| dx is equal to

    Text Solution

    |

  16. Let f(x)={(1-|x|","|x|le1),(0","|x|gt1):} and g(x)=f(x-1)"for all" x i...

    Text Solution

    |

  17. Let f(x)={1-|x|,|x| leq 1 and 0,|x| lt 1 and g(x)=f(x-)+f(x + 1), for...

    Text Solution

    |

  18. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

    Text Solution

    |

  19. If In=int-pi^pi (sinnx)/((1+pi^x)sinx)dx, n=0,1,2, …, then (A) In=I(n+...

    Text Solution

    |

  20. If In=int-pi^pi (sinnx)/((1+pi^x)sinx)dx, n=0,1,2, …, then (A) In=I(n+...

    Text Solution

    |