Home
Class 12
MATHS
If I(n)=int(0)^(pi//4) tan^(n)theta d th...

If `I_(n)=int_(0)^(pi//4) tan^(n)theta d theta`, then `I_(8)+I_(6)` equals

A

`(1)/(4)`

B

`(1)/(5)`

C

`(1)/(6)`

D

`(1)/(7)`

Text Solution

Verified by Experts

The correct Answer is:
D
We have, `I_(n)=overset(pi//4)underset(0)int tan^(n)theta d theta`
`:. I_(8)+I_(6)=overset(pi//4)underset(0)int(tan^(8)theta+tan^(6)theta)d theta`
`rArr_(8)+I_(6)=overset(pi//4)underset(0)int tan^(6)theta sec^(2)theta d theta=overset(1)underset(0)t^(6) dt`, where `t=tan theta`
`rArrI_(8)+I_(6)[(t^(7))/(7)]_(0)^(1)=(1)/(7)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|145 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|12 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

int_(0)^(pi//8) cos^(3)4 theta d theta=

If I_(n)=int_(0)^((pi)/(4))tan^(n)theta then I_(8)+I_(6) equals

If I_(n)=int_(0)^(pi//4)tan^(n)x dx, then 7(I_(6)+I_(8))=

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

If I_(n)=int_(0)^(pi//2) x^(n) sin x dx , then I_(4)+12I_(2) is equal to\

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

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

OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 2
  1. If I(n)=int(0)^(pi//4) tan^(n)theta d theta, then I(8)+I(6) equals

    Text Solution

    |

  2. The integral int(0)^(r pi) sin^(2x)x dx is equal to

    Text Solution

    |

  3. The value of the integral int(0)^(2)x[x]dx

    Text Solution

    |

  4. The value of integral sum (k=1)^(n) int (0)^(1) f(k - 1+x) dx is

    Text Solution

    |

  5. Let f(x) be a funntion satifying f'(x)=f(x) with f(0)=1 and g(x) be th...

    Text Solution

    |

  6. If I=int(0)^(1) cos{ 2 "cot"^(-1)sqrt((1-x)/(1+x))}dx then

    Text Solution

    |

  7. The value of int(a)^(a+(pi//2))(sin^(4)x+cos^(4)x)dx is

    Text Solution

    |

  8. The vaue of int(-1)^(2) (|x|)/(x)dx is

    Text Solution

    |

  9. The value of int0^1 (x^(3))/(1+x^(8))dx is

    Text Solution

    |

  10. The value of int(0)^(3) xsqrt(1+x)dx, is

    Text Solution

    |

  11. The value of the integral int(0)^(1) log sin ((pix)/(2))dx is

    Text Solution

    |

  12. The value of the integral int(0)^(pi)x log sin x dx is

    Text Solution

    |

  13. If I(1)=int(0)^(oo) (dx)/(1+x^(4))dx and I(2)underset(0)overset(oo)in...

    Text Solution

    |

  14. If f(x)={{:(x,"for " x lt 1),(x-1,"for " x ge1):},"then" int(0)^(2) x...

    Text Solution

    |

  15. The value of the integral int(0)^(2) (1)/((x^(2)+1)^(3//2))dx is

    Text Solution

    |

  16. If int(0)^(2a) f(x)dx=int(0)^(2a) f(x)dx, then

    Text Solution

    |

  17. If int(0)^(36) (1)/(2x+9)dx =log k, is equal to

    Text Solution

    |

  18. The value of the integral int(0)^(pi//2) sin^(6) x dx, is

    Text Solution

    |

  19. If int(0)^(oo) e^(-x^(2))dx=sqrt((pi)/(2))"then"int(0)^(oo) e^(-ax^(2)...

    Text Solution

    |

  20. The value of the integral int 0^oo 1/(1+x^4)dx is

    Text Solution

    |

  21. If int(pi//2)^(x) sqrt(3-2sin^(2)u) dx+int(dx)^(dy) equal pi//2

    Text Solution

    |