Home
Class 12
MATHS
Suppose that F(x) is an anti-derivative ...

Suppose that `F(x)` is an anti-derivative of `f(x)=(sinx)/x ,w h e r ex > 0.` Then `int_1^3tan^(-1)dx` can be expressed as `F(6)-F(2)` (b) `1/2(F(6)-f(2))` `1/2(F(3)-f(1))` (d) `2(F(6))-F(2))`

A

`F(6)-F(2)`

B

`(1)/(2)[F(6)-F(2)]`

C

`(1)/(2)[F(3)-F(1)]`

D

`2[F(6)-F(2)]`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Objective Type Questions (More than one answer)|32 Videos
  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Linked Comprehension Type Questions|11 Videos
  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Competition level Questions|80 Videos
  • DIFFERENTIAL EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section - J (Aakash Challengers Questions)|4 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT (SECTION - J)(ANKASH CHALLENGERS QUESTIONS)|4 Videos

Similar Questions

Explore conceptually related problems

Find the anti derivative F of f defined by f(x)=4x^3-6 , where F (0) = 3

Find the derivative of f(x)=2x^2+3x-5 at x=-1 . Also, prove that f'(0)+3f'(-1)=0.

Let F(x)""=""f(x)""+""f(1/x),"w h e r e"f(x)=int_1^x(logt)/(1+t)dtdot Then 2F(x)""= (1) 1/2 (2) 0 (3) 1 (4) 2

If f(1) = 1, f'(1) = 3, then the derivative of f(f(x))) + (f(x))^(2) at x = 1 is

Let f(x) be a function defined on R satisfyin f(x) =f(1-x) for all x in R . Then int_(-1//2)^(1//2) f(x+(1)/(2))sin x dx equals

Given f(x)=4x^8 , then (a) f'(1/2)=f'(-1/2) (b) f(1/2)=-f'(-1/2) (c) f'(-1/2)=-f'(1/2) (d) f(1/2)=f'(-1/2)

Let d/(dx) (F(x))= e^(sinx)/x, x>0 . If int_1^4 2e^sin(x^2)/x dx = F(k)-F(1) , then possible value of k is:

If f:R->R be defined by f(x)=x^2+1 , then find f^(-1)(17) and f^(-1)(-3) .

If f(x)=2^(x),"then"f(0),f(1),f(2)..."are in"

If f(x)=log((1+x)/(1-x)),t h e n (a) f(x_1)f(x_2)=f(x_1+x_2) (b) f(x+2)-2f(x+1)+f(x)=0 (c) f(x)+f(x+1)=f(x^2+x) (d) f(x_1)+f(x_2)=f((x_1+x_2)/(1+x_1x_2))

AAKASH INSTITUTE ENGLISH-INTEGRALS-Objective Type Questions (Only one answer)
  1. underset(kto0) lim1/kint0^k(1+sin2x)^(1/x)dx

    Text Solution

    |

  2. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

    Text Solution

    |

  3. Suppose that F(x) is an anti-derivative of f(x)=(sinx)/x ,w h e r ex >...

    Text Solution

    |

  4. If f(x)=[{:(sqrt(1-x), , , 0 le x le 1),((7x-6)^(-1) , , ,1 le x le 2)...

    Text Solution

    |

  5. If f:RrarrR defined by f(x)=sinx+x, then find the value of int0^pi(f^-...

    Text Solution

    |

  6. The value of int0^100 [tan^-1 x]dx is, (where [*] denotes greatest in...

    Text Solution

    |

  7. Iff(x)={0,w h e r ex=n/(n+1),n=1,2,31,e l s e w h e r e t h e nt h ev...

    Text Solution

    |

  8. Let g(x) be a continous and differentiable function such that int(0...

    Text Solution

    |

  9. Let d/(dx)F(x)=(e^(sinx))/x . x lt0. If int(1)^(4)(2e^(sinx^(2)))/xdx=...

    Text Solution

    |

  10. f:(0,infty)rarrR and F(x)=int(0)^(x)t f(t)dt If F(x^(2))=x^(4)+x^(5)...

    Text Solution

    |

  11. int(-pi//4) ^(pi//4) x^(3) sin^(4) xdx=

    Text Solution

    |

  12. The value of int(-10)^(10)[{f(f(x)}+{f(f((1)/(x))}]dx, where f(x)=(1-x...

    Text Solution

    |

  13. The value of int(-2)^(2)(ax^(2011)+bx^(2001)+c)dx, where a, b, c are c...

    Text Solution

    |

  14. If for non zero x, 3f(x)+4f((1)/(x))=(1)/(x)-10, then the value of int...

    Text Solution

    |

  15. The value of int(2010pi+(pi)/(6))^(2010pi+(pi)/(3))(sinx+cosx)dx is

    Text Solution

    |

  16. Let int(a)^(b)f(x)dx=int(a+c)^(b+c)f(x-c)dx. Then the value of int(0)^...

    Text Solution

    |

  17. If x^(f(x))=e^(x-f(x)), then the value of integral int(1)^(2)f'(x){(1+...

    Text Solution

    |

  18. If overset(x)underset(e )int t f(t)dt=sin x-x cos x-(x^(2))/(2) for al...

    Text Solution

    |

  19. The value of the integral int(-2012pi)^(2012pi) {d/dx(int0^(x^2) cost^...

    Text Solution

    |

  20. The value of int(-2010pi)^(2010pi) {x^2011(1+tan(pi/3-x)(1+tan(x-pi/1...

    Text Solution

    |