Home
Class 12
MATHS
Let f(x)=int x^2/((1+x^2)(1+sqrt(1+x^2))...

Let `f(x)=int x^2/((1+x^2)(1+sqrt(1+x^2)))dx` and `f(0)=0` then `f(1)` is

A

`log_(e)(1+sqrt(2))`

B

`log_(e)(1+sqrt(2))-pi/4`

C

`log_(e)(1+sqrt(2))+pi/4`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|5 Videos

  • INDEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|5 Videos

  • INDEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 6|10 Videos

  • HYPERBOLA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|17 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos

Similar Questions

Explore conceptually related problems

" If "f(x)=int(x^(2)dx)/((1+x^(2))(1+sqrt(1+x^(2))))" and "f(0)=0" Find the value of "f(sqrt(3))-ln(2+sqrt(3))

Let f(x)=int(1)/((1+x^(2))^(3//2))dx and f(0)=0 then f(1)=

If f(x)=int 2-(1)/(1+x^(2))-(1)/(sqrt(1+x^(2)))dx , then f is

f(x) = int(x^(2)+x+1)/(x+1+sqrt(x))dx , then f(1) =

If f(x)=int(3x^(2)+1)/((x^(2)-1)^(3))dx and f(0)=0, then the value of (2)/(f(2))| is

If f(x)+int{f(x)}^(-2)dx=0 and f(1)=0 then f(x) is

Let F(x)=(1)/(2)int(sin x+cos x)/(e^(-x)+sin x)dx and F(0)=1 then F(x) is

If f(x)=int(3x^4-1)/(x^4+x+1)^2dx and f(0)=0 , then f(-1)= …

If int1/((1+x^(2))sqrt(1-x^(2)))dx=F(x)+c " and " F(1)=0 , then for x gt 0, F(x)=

ARIHANT MATHS-INDEFINITE INTEGRAL -Exercise (Single Option Correct Type Questions)
  1. Let f(x)=int x^2/((1+x^2)(1+sqrt(1+x^2)))dx and f(0)=0 then f(1) is

    Text Solution

    |

  2. If intf(x)dx=f(x), then int{f(x)}^2dx is equal to

    Text Solution

    |

  3. If int f(x)dx=F(x), then intx^3f(x^2)dx is equal to :

    Text Solution

    |

  4. If n is a positive odd integer, then int |x^n| dx=

    Text Solution

    |

  5. Let F(x) be the primitive of (3x+2)/sqrt(x-9)w.r.t.x. If F(10)=60 then...

    Text Solution

    |

  6. int(x^x)^x(2xlogex+x)dx is equal to

    Text Solution

    |

  7. The value of int x log x (log x - 1) dx is equal to

    Text Solution

    |

  8. int (x^2 -1 )/ (x^3 sqrt(2x^4 - 2x^2 +1))dx is equal to

    Text Solution

    |

  9. Let f(x) be a polynomial satisfying f(0)=2 , f'(0)=3 and f''(x)=f(x) t...

    Text Solution

    |

  10. int(e^((x^2+4lnx))-x^3e^(x^2))/(x-1) dx is equal to

    Text Solution

    |

  11. int tan^(4)x dx = A tan^(3) x+ B tan x + f(x), then

    Text Solution

    |

  12. If the anti derivative of int sin^4x/x dx is f(x) then int(sin^4(p+q)...

    Text Solution

    |

  13. Prove that : sintheta/cos[3theta]+sin[3theta]/cos[9theta]+sin[9theta...

    Text Solution

    |

  14. If x^2!=n pi-1, n in N. Then, the value of int x sqrt((2sin(x^2+1)-sin...

    Text Solution

    |

  15. int(dx)/(cos(2x)cos(4x))=

    Text Solution

    |

  16. int(1-7cos^(2)x)/(sin^(7)xcos^(2)x)dx=(f(x))/((sinx)^(7))+C, then f(x)...

    Text Solution

    |

  17. Evaluate: (sin^3x dx)/((cos^4x+3cos^2x+1)tan^(-1)(secx+cosx)

    Text Solution

    |

  18. The primitive of the function f(x)= x | cos x|, when pi/2 lt x lt pi i...

    Text Solution

    |

  19. The primitive of the function f(x)=(2x+1)|sin x|, when pi lt x lt 2 p...

    Text Solution

    |

  20. If f(x)=|(0,x^2-sinx,cosx-2),(sinx-x^2,0,1-2x),(2-cosx,2x-1,0)|,then i...

    Text Solution

    |