Home
Class 12
MATHS
if ngt1and I=int0^infty dx/((x+sqrt(1+x^...

if `ngt1`and `I=int_0^infty dx/((x+sqrt(1+x^2))^n` then I equals

A

`n/(n^2-1)`

B

`2n/(n^2-1)`

C

`n/(2(n^2-1)`

D

`sqrtn^2-1`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY & DIFFERENTIABILITY

    PATHFINDER|Exercise QUESTION BANK|13 Videos
  • DETERMINATES

    PATHFINDER|Exercise QUESTION BANK|21 Videos

Similar Questions

Explore conceptually related problems

if I=int_8^15 dx/((x-3)sqrt(x+1)) then I equals

IfI=int(dx)/(x^3sqrt(x^2-1)) , the equals

if b gt a and I=int_a^b dx/(sqrt((x-a)(b-x) then I equals

if 0ltalphalt1 and I=int_(-1)^1dx/(sqrt(1-2alphax+alpha^2) then I equals

If I= int_0^(pi/2) dx/(sqrt(1+sin^3x) then

if I=int_0^a sqrt((a-x)/(a+x))dx, agt0 Then I equals

int_(0)^(oo)(dx)/([x+sqrt(1+x^(2))]^(n)

int dx/((1+sqrtx)sqrt(x-x^2) is equal to ?

I=int_(-2)^2(abs(1-x^4))dx then I equals

If I=int sqrt((5-x)/(2+x)) dx, then equal

PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. If intsin^4x/(cos^8x)dx= atan^7x+btan^5x+c then find the relation betw...

    Text Solution

    |

  2. The value of x satisfying int0^(2[x+14]){x/2}dx=int0^({x})[x+14]dxis e...

    Text Solution

    |

  3. if ngt1and I=int0^infty dx/((x+sqrt(1+x^2))^n then I equals

    Text Solution

    |

  4. If [x] denotes the greatest integer lex and n inN then value of In=int...

    Text Solution

    |

  5. if I=int0^1dx/((1+x)(2+x)sqrtx(1-x)then I equals

    Text Solution

    |

  6. if int0^1 x(1-x)^(2007//2)dx then it equals

    Text Solution

    |

  7. if I=int(-1)^2abs(xsinpix)dx then I equals

    Text Solution

    |

  8. if I=int(alpha)^(beta)[loglogx+1/(logx)^2]dx then I equals

    Text Solution

    |

  9. if I=int0^(pi/4) (sin2theta)/(sin^2theta+cos^4theta)d(theta) then I eq...

    Text Solution

    |

  10. if 0ltalphalt1 and I=int(-1)^1dx/(sqrt(1-2alphax+alpha^2) then I equal...

    Text Solution

    |

  11. if I=int8^15 dx/((x-3)sqrt(x+1)) then I equals

    Text Solution

    |

  12. underset(xrarr(pi//4))lim( int2^(sec^2x)(f(t)dt))/(x^2-(pi)^2/16 equal...

    Text Solution

    |

  13. If int1^infty((x^3+3)dx)/(x^6(x^2+1))=(a+bpi)/c, then

    Text Solution

    |

  14. If int0^1 ((1-x^2)dx)/(1+x^2+x^4) =aInb then,

    Text Solution

    |

  15. If f(x)=int(-2)^xabs(t+1)dt then,

    Text Solution

    |

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

    Text Solution

    |

  17. Let In=int0^(pi/4)tan^nxdx, then 1/(I2+I4),1/(I3+I5), 1/(I4+I6), 1/(I5...

    Text Solution

    |

  18. The maximum and minimum values of the integral int0^(pi/2)dx/(1+sin^2x...

    Text Solution

    |

  19. Let f(x)=int0^xabs(sint)dt, then

    Text Solution

    |

  20. The value of int(pisinmxsinnxdx(m,ninN) is equal to for limits-pi to p...

    Text Solution

    |