Home
Class 12
MATHS
If f(x) =int (x^2+sin^2x)/(1+x^2) sex^2x...

If `f(x) =int (x^2+sin^2x)/(1+x^2) sex^2x dx and f(0) =0 then f(1) =`

A

`1-(pi)/(4)`

B

`(pi)/(4)`

C

`tan 1+(pi)/(4)`

D

`tan1+1`

Text Solution

Verified by Experts

The correct Answer is:
C
We have , `f(x)=int {((x^(2)+1)+(1-sin^(2)x))/(1+x^(2))}sec^(2)x dx`
`rArrf(x)=int(sec^(2)x+(1)/(1+x^(2)))dx`
`rArrf(x)=tanx+tan^(-1)x+C`
`thereforef(0)=0rArrC=0`
Hence , `f(x) tanx+tan^(-1)x`
`rArrf(1)=tan1+(pi)/(4)`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|3 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Exercise|62 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • INCREASING AND DECREASING FUNCTIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|20 Videos

  • INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Illustration|1 Videos

Similar Questions

Explore conceptually related problems

f(x)=int(x^(2)+sin^(2)x)/(1+x^(2))sex^(2)xdx and f(0)=0then f(1)=

If f(x)=int(x^(2)+sin^(2)x)/(1+x^(2))sec^(2)xdx and f(0)=0, then f(1)=

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

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

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

If F(x)=int(x+sin x)/(1+cos x)dx and F(0)=0 then the value of f((pi)/(2)) is

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 int e^(sin x)(x cos^(3)x-sin x)/(cos^(2)x)dx and f(0)=1 then f(pi)= is

If f'(x) = f(x)+ int _(0)^(1)f (x) dx and given f (0) =1, then int f (x) dx is equal to :

f(x)=(sin x-x cos x)/(x^(2)) if x!=0 and f(0)=0 then int_(0)^(1)f(x)dx is

OBJECTIVE RD SHARMA-INDEFINITE INTEGRALS-Solved Example
  1. The value of int(sin^(2)xcos^(2)x)/((sin^(3)x+cos^(3)x)^(2))dx , is

    Text Solution

    |

  2. The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitr...

    Text Solution

    |

  3. If f(x) =int (x^2+sin^2x)/(1+x^2) sex^2x dx and f(0) =0 then f(1) =

    Text Solution

    |

  4. At present, a firm is manufacturing 2000 items. It is estimated tha...

    Text Solution

    |

  5. If int f(x)dx=psi(x), then int x^5f(x^3)dx

    Text Solution

    |

  6. The integral int(1+x-1/x)e^(x+1/x)dx is equal to

    Text Solution

    |

  7. if int(1-5sin^2x)/(cos^5xsin^2x)dx=f(x)/(cos^5x)+c then f(x)

    Text Solution

    |

  8. int(x^(7m)+x^(2m)+x^m)(2x^(6m)+7x^m+14)^(1/m)dx

    Text Solution

    |

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

    Text Solution

    |

  10. intsqrt(x-3)(sin^(-1)(Inx)+cos^(-1)(Inx))dx is equal to

    Text Solution

    |

  11. The integral int(1+x-1/x)e^(x+1/x)dx is equal to

    Text Solution

    |

  12. int e^(x^4) (x + x^3 +2x^5) e^(x^2) dx is equal to

    Text Solution

    |

  13. int[sin(101 x)*sin^(99)x]dx

    Text Solution

    |

  14. Suppose int(1-7cos^2x)/(sin^7xcos^2x)dx=(g(x))/(sin^7x)+c where C is a...

    Text Solution

    |

  15. int(x^(2)+x)(x^(-8)+2x^(-9))^(1//10)dx is equal to

    Text Solution

    |

  16. If int 2/(2-x)^2 ((2-x)/(2+x))^(1//3)\ dx = lambda ((2+x)/(2-x))^mu + ...

    Text Solution

    |

  17. Let f(x) be a quadratic function such that f(0)=1 and int(f(x))/(x^2(x...

    Text Solution

    |

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

    Text Solution

    |

  19. inte^(x)((x-1)(x-logx))/(x^(2))dx is equal to

    Text Solution

    |

  20. If I=intx^(27)(6x^(2)+5x+4)(x^(2)+x+1)^(6)dx=f(x)+C, then f(x) is eq...

    Text Solution

    |