Home
Class 12
MATHS
If f(x) = int(x)^(x^(2)) t^(2)lnt then f...

If `f(x) = int_(x)^(x^(2)) t^(2)lnt` then find `f'(e)`

Text Solution

Verified by Experts

The correct Answer is:
`e^(2)(6e-1)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 1|31 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 1 Part-II|55 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

  • DPP

    RESONANCE|Exercise QUESTION|665 Videos

Similar Questions

Explore conceptually related problems

If F(x) = int_(x^(2))^(x^(3))(1)/(lnt) dt then find F'(e )

If f(x)=int_(x^(2))^(x^(2)+1)e^(-t^(2))dt , then find the interval in which f(x) increases.

If f(x)= int_(x^2)^(x^(2) +4) e^(-t^(2) ) dt , then the function f(x) increases in

If int_(0)^(x^(2)(1+x))f(t)dt = x then find f(2)

f(x) = int_(x)^(x^(2))(e^(t))/(t)dt , then f'(t) is equal to :

If int_(0)^(x)f(t)dt = x^(2)-int_(0)^(x^(2))(f(t))/(t)dt then find f(1) .

If f(x)=int_(x)^(x+1) (e^-(t^2)) dt, then the interval in which f(x) is decreasing is

RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Self practive problem
  1. Find the equation of tangent to the y = F(x) at x = 1, where F(x) = i...

    Text Solution

    |

  2. If int(0)^(x)f(t)dt = x^(2)-int(0)^(x^(2))(f(t))/(t)dt then find f(1).

    Text Solution

    |

  3. If f(x) = int(x)^(x^(2)) t^(2)lnt then find f'(e)

    Text Solution

    |

  4. If y = int(4)^(4x^(2))t^(4)e^(4t)dt, find (d^(2)y)/(dx^(2))

    Text Solution

    |

  5. If y = int(0)^(x^(2))ln(1+t), then find (d^(2)y)/(dx^(2))

    Text Solution

    |

  6. If int(0)^(x^(2)(1+x))f(t)dt = x then find f(2)

    Text Solution

    |

  7. Evaluate int(0)^(pi)ln(1+bcosx) dx, 'b' being parameter.

    Text Solution

    |

  8. int(pi//2)^(0)sin^(11)xdx

    Text Solution

    |

  9. int(0)^(-pi//2)sin^(5)xcos^(4)xdx

    Text Solution

    |

  10. int(0)^(1) x^(5)sin^(-1)xdx

    Text Solution

    |

  11. int(0)^(9) x(a^(2)-x^(2))^(7/2)dx

    Text Solution

    |

  12. int(0)^(2) sqrt(2-x)dx.

    Text Solution

    |

  13. Prove the following : int(0)^(1)e^(-x)cos^(2)xdx lt int(0)^(1)e^(-x^(2...

    Text Solution

    |

  14. Prove the following : 0 lt int(0)^(pi//2)sin^(n+1)xdx lt int(0)^(pi//2...

    Text Solution

    |

  15. Prove the following : e^(-(1)/(e)) lt int(0)^(1)x^(x)dx lt 1

    Text Solution

    |

  16. Prove the following: -1/2lt=int0^1(x^3cosx)/(2+x^2)dx<1/2

    Text Solution

    |

  17. Prove the following : 1 lt int(0)^(pi//2)sqrt(sinx)dx lt sqrt(pi/2)

    Text Solution

    |

  18. Prove the following : 4/pi lt int(pi/4)^(pi/3) (tanx)/(x) lt (3sqrt(3)...

    Text Solution

    |

  19. lim(nrarroo) {1/n+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+"......"+1/(...

    Text Solution

    |

  20. lim(nrarroo) [1/(1+n)+(1)/(2+n)+(1)/(3+n)+"....."+(1)/(5n)]

    Text Solution

    |