Home
Class 12
MATHS
If f(x) is differentiable and int0^(t^2)...

If `f(x)` is differentiable and `int_0^(t^2) x f(x) dx=2/5t^5,` then `f(4/(25))` equals (a)`2/5` (b) `-5/2` (c)`1` (d) `5/2`

A

`2//5`

B

`-5//2`

C

1

D

`5//2`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • INTEGRAL CALCULUS - 2

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

    VMC MODULES ENGLISH|Exercise Level - 1|190 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 int_(0)^(x)f(t)dt=x^2+int_(x)^(1)\ t^2\ f(t)dt , then f((1)/(2)) is equal to (a) (24)/(25) (b) (4)/(25) (c) (4)/(5) (d) (2)/(5)

If a curve y=f(x) passes through the point (1,-1) and satisfies the differential equation ,y(1+x y)dx""=x""dy , then f(-1/2) is equal to: (1) -2/5 (2) -4/5 (3) 2/5 (4) 4/5

Iff(2-x)=f(2+x)a n df(4-x)=f(4+x) for all xa n df(x) is a function for which int_0^2f(x)dx=5,t h e nint_0^(50)f(x)dx is equal to (a)125 (b) int_(-4)^(46)f(x)dx (c) int_1^(51)f(x)dx (d) int_2^(52)f(x)dx

If f(x) is an invertible function and g(x)=2f(x)+5, then the value of g^(-1)(x)i s (a) 2f^(-1)(x)-5 (b) 1/(2f^(-1)(x)+5) 1/2f^(-1)(x)+5 (d) f^(-1)((x-5)/2)

If f(x) is an invertible function and g(x)=2f(x)+5, then the value of g^(-1)(x)i s (a) 2f^(-1)(x)-5 (b) 1/(2f^(-1)(x)+5) 1/2f^(-1)(x)+5 (d) f^(-1)((x-5)/2)

Let f(x) be a differentiable function such that int_(t)^(t^(2))xf(x)dx=(4)/(3)t^(3)-(4t)/(3)AA t ge0 , then f(1) is equal to

If 2f(x)-3f(1/x)=x^2(x!=0), then f(2) is equal to (a) -7/4("b")""5/2 (c) -1 (d) none of these

f(x) = int_(x)^(x^(2))(e^(t))/(t)dt , then f'(t) is equal to : (a) 0 (b) 2e (c) 2e^2 -2 (d) e^2-e

If f is continuous function and F(x)=int_0^x((2t+3)*int_t^2f(u)d u)dt , then |(F''(2))/(f(2))| is equal to_____

Differentiate the following w.r.t x x^(5//2)

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Main (Archive)
  1. The intercepts on x- axis made by tangents to the curve, y=int(0)^(x)|...

    Text Solution

    |

  2. Ifint(sinx)^1t^2f(t)dt=1-sinx ,w h e r e .x in (0,pi/2), then find th...

    Text Solution

    |

  3. If f(x) is differentiable and int0^(t^2) x f(x) dx=2/5t^5, then f(4/(2...

    Text Solution

    |

  4. If f(x)=int(x^2)^(x^2+1)e^(-t^2)dt , then f(x) increases in

    Text Solution

    |

  5. If I(m,n)=int0^1 t^m(1+t)^n.dt, then the expression for I(m,n) in term...

    Text Solution

    |

  6. Let f(x)=int(1)^(x) sqrt(2-t^(2)) dt, then the real roots of the equa...

    Text Solution

    |

  7. Let f: (0, infty) rarr R and F (x) = int(0) ^(x) f(t) dt . If F(x^(2)...

    Text Solution

    |

  8. The area of the quadrilateral formed by the tangents at the endpoint o...

    Text Solution

    |

  9. The area bounded by the curves y = |x| - 1 and y = -|x| +1 is equal to

    Text Solution

    |

  10. about to only mathematics

    Text Solution

    |

  11. int(-1)^(1)(x^2+1)dx is equal to

    Text Solution

    |

  12. The area (in sq. units) of the region described by {x,y):y^(2)le2x and...

    Text Solution

    |

  13. The area of the region described by A={(x,y):x^(2)+y^(2)le1 and y^(2)l...

    Text Solution

    |

  14. The area (in square units) bounded by the curves y=sqrt(x),2y-x+3=0, x...

    Text Solution

    |

  15. The area bounded by the curves y=(x-1)^(2),y=(x+1)^(2) " and " y=(1)/(...

    Text Solution

    |

  16. If the area enclosed between the curves y=a x^2a n dx=a y^2(a >0) is 1...

    Text Solution

    |

  17. If the area bounded by the curve y=f(x), x-axis and the ordinates x=1 ...

    Text Solution

    |

  18. about to only mathematics

    Text Solution

    |

  19. The area (in sq. units) bounded by the parabola y=x^2-1, the tangent a...

    Text Solution

    |

  20. The value of int(0)^(pi)|cos x|^(3)dx is :

    Text Solution

    |