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

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 ?

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

Promotional Banner

Topper's Solved these Questions

  • Miscellaneous Exercises

    A DAS GUPTA|Exercise Exercise|77 Videos

  • Pair of Straight Lines and Transformation of Axes

    A DAS GUPTA|Exercise EXERCISE|22 Videos

Similar Questions

Explore conceptually related problems

If I_(n)=int_(-pi)^( pi)(sin nx)/((1+pi^(x))sin x)dx,n=0,1,2 then which one of the following is not true?

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

If I_(1)=int_(0)^(pi//2) x sin x dx and I_(2) = int_(0)^(pi//2) x cos x dx ,then which one of the following is true ?

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

If I=int_(0)^(1//2) (1)/(sqrt(1-x^(2n)))dx then which one of the following is not true ?

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

int_(0)^(pi)(dx)/((1+sinx))=?

A DAS GUPTA-Objective Tests-Exercise
  1. An ellipse intersects the hyperbola 2x^(2)-2y^(2)=1 orthogonally. The ...

    Text Solution

    |

  2. Let L = lim(x rarr 0) ( a - sqrt( a^2 - x^2) - x^2/4)/x^4, a>0.If L is...

    Text Solution

    |

  3. For the function f(x)=x "cos" 1/x, x ge1

    Text Solution

    |

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

    Text Solution

    |

  5. The area of the region bounded by the curve y=e^(x) and lines x=0 and ...

    Text Solution

    |

  6. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

    Text Solution

    |

  7. Let S={1,,2,34} . The total number of unordered pairs of disjoint s...

    Text Solution

    |

  8. For r= 0, 1,.....,10, let Ar,Br, and Crdenote, respectively, the coe...

    Text Solution

    |

  9. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

    Text Solution

    |

  10. If the angle A , B and C of a triangle are in arithmetic progession an...

    Text Solution

    |

  11. Two adjacent sides of a parallelogram A B C D are given by vec A B...

    Text Solution

    |

  12. The equation of the plane containing the straight line x/2=y/3=z/4 and...

    Text Solution

    |

  13. If the distance of the point P(1,-2,1) from the plane x+2y-2z=alpha...

    Text Solution

    |

  14. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  15. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  16. Let omega be a complex cube root unity with omega!=1. A fair die is th...

    Text Solution

    |

  17. A signal which can be green or red with probability 4/5 and 1/5 respec...

    Text Solution

    |

  18. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+iz(2...

    Text Solution

    |

  19. Let ABC be a triangle such that angleACB=pi/6 and let a , b and c deno...

    Text Solution

    |

  20. Let A and B be two distinct points on the parabola y^2 = 4x. If the ax...

    Text Solution

    |