Home
Class 12
MATHS
Iff(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+...

`Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4),` then find the value of `f^(prime)(2)`

A

0

B

`(1)/(17)`

C

`(3)/(17)`

D

`(2)/(17)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|64 Videos
  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|103 Videos
  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|103 Videos
  • FUNCTIONS

    VMC MODULES ENGLISH|Exercise JEE Main & Advanced|8 Videos
  • INTEGRAL CALCULUS-1

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|25 Videos

Similar Questions

Explore conceptually related problems

If ("lim")_(tvecx)(e^tf(x)-e^xf(t))/((t-x)(f(x))^2)=2a n df(0)=1/2, then find the value of f^(prime)(0)dot 4 (b) 2 (c) 0 (d) 1

If f(x)=1+1/x int_1^x f(t) dt, then the value of f(e^-1) is

f(x)=int_1^x(tan^(-1)(t))/t dt \ AAx in R^+, then find the value of f(e^2)-f(1/(e^2))

If lim_(trarrx)(e^(t)f(x)-e^(x)f(t))/((t-x)(f(x))^(2))=2 andf(0)=(1)/(2), then find the value of f'(0).

If lim_(trarrx) (e^(t)f(x)-e^(x)f(t))/((t-x)(f(x))^(2))=2 andf(0)=(1)/(2), then find the value of f'(0).

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of (lim)_(xvec0)(((dy)/(dz)))/x

Iff(x)=int_((x^2)/(16))^(x^2)(sinxsinsqrt(theta))/(1+cos^2sqrt(theta))d theta, then find the value of f^(prime)(pi/2)dot

Given a function g, continous everywhere such that g (1)=5 and int _(0)^(1) g (t) dt =2. If f (x) =1/2 int _(0) ^(x) (x -t)^(2) g (t) dt, then find the value of f '(1)+f''(1).

Evaluate: int_(-1)^4f(x)dx=4a n dint_2^4(3-f(x))dx=7, then find the value of int_2^(-1)f(x)dxdot

Evaluate: int_(-1)^4f(x)dx=4a n dint_2^4(3-f(x))dx=7, then find the value of int_-1^(2)f(x)dxdot

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -Level - 1
  1. If (d)/(dx)f(x)=g(x) for a le x le b then, overset(b)underset(a)int f...

    Text Solution

    |

  2. If underset(1)overset(x)int(dt)/(|t|sqrt(t^(2)-t)) = (pi)/(6), then x ...

    Text Solution

    |

  3. Iff(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+t^4), then find the value of ...

    Text Solution

    |

  4. If x=int(0)^(y)(dt)/(sqrt(1+9t^(2)))and (d^(2)y)/(dx^(2))=a^(2)y then ...

    Text Solution

    |

  5. f(x)=int0^x f(t) dt=x+intx^1 tf(t)dt, then the value of f(1) is

    Text Solution

    |

  6. If f(x)=cosx-int0^x(x-t)f(t)dt ,t h e nf^(prime)(x)+f(x) is equal to -...

    Text Solution

    |

  7. If f(-x)+f(x)=0 then inta^x f(t) dt is

    Text Solution

    |

  8. If int0^af(2a-x)dx=m and int0^af(x)dx=n, then int0^(2a) f(x) dx is equ...

    Text Solution

    |

  9. If f(y)=e^(y),g(y)=y,ygt0 and F(t)=int(0)^(1)f(t-y)g(y)dt then

    Text Solution

    |

  10. lim(x to 0)(int(0)^(x^(2))(tan^(-1)t)dt)/(int(0)^(x^(2))sin sqrt(t)dt)...

    Text Solution

    |

  11. Find the points of maxima /minima of int(0)^(x^(2))(t^(2)-5t+4)/(2+e^(...

    Text Solution

    |

  12. Let f(x)=underset(0)overset(x)int |xx-2|dx, ge 0. Then, f'(x) is

    Text Solution

    |

  13. If x=int(c^(2))^(tan t)tan^(-1)z dz, y= int(n)^(sqrt(t))(cos(z^(2)))/(...

    Text Solution

    |

  14. Area of the ellipse x^2/a^2+y^2/b^2=1is piab

    Text Solution

    |

  15. Prove that the area in the first quadrant enclosed by the axis, the ...

    Text Solution

    |

  16. Find the area bounded by the curve x^2=4y and the straight line x=4y-2...

    Text Solution

    |

  17. Find the area of the figure bounded by the parabolas x=-2y^2, x=1-3y^2...

    Text Solution

    |

  18. Find the area bounded by the parabola y=2-x^2 and the straight line y+...

    Text Solution

    |

  19. Calculate the area enclosed by the parabola y^(2)=x+3y and the Y-axis...

    Text Solution

    |

  20. Prove that the area bonded by the parabola y^2=5x+6 and x^2=y is 81/1...

    Text Solution

    |