Home
Class 12
MATHS
Let d/(dx)F(x)=(e^(sinx))/x . x lt0. If ...

Let `d/(dx)F(x)=(e^(sinx))/x . x lt0`. If `int_(1)^(4)(2e^(sinx^(2)))/xdx=F(k)-F(1)` then find the possible value of `k`.

Text Solution

Verified by Experts

The correct Answer is:
k = 16
Promotional Banner

Topper's Solved these Questions

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|64 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

Let (d)/(dx) F(x)=(e^(sin x))/(x), x gt 0 , If int_(1)^(4) (3)/(x) e^(sin x^(3))dx=F(k)-F(1) , then one of the possible value of k is -

Let d/(dx)F(x)=((e^(sinx))/x),x > 0. If int_1^4 3/x e^sin (x^3)dx=F(k)-F(1), then one of the possible values of k , is: (a) 15 (b) 16 (c) 63 (d) 64

Let d/(dx)F(x)=((e^(sinx))/x),x > 0. If int_1^4 3/x e^sin x^3dx=F(k)-F(1), then one of the possible values of k , is: 15 (b) 16 (c) 63 (d) 64

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:

Let y =f (x) satisfies the differential equation xy (1+y) dx =dy . If f (0)=1 and f (2) =(e ^(2))/(k-e ^(2)), then find the value of k.

If int(1+xcosx)/(x(1-x^(2)e^(2sinx)))dx = k" ln "sqrt((x^(2)e^(2 sinx))/(1-x^(2)e^(2sinx)))+C then k is equal to:

If 2f(x)+f(-x)=1/xsin(x-1/x) then the value of int_(1/e)^e f(x)d x is

Suppose f, f' and f'' are continuous on [0, e] and that f'(e )= f(e ) = f(1) = 1 and int_(1)^(e )(f(x))/(x^(2))dx=(1)/(2) , then the value of int_(1)^(e ) f''(x)ln xdx equals :

Suppose f, f' and f'' are continuous on [0, e] and that f'(e )= f(e ) = f(1) = 1 and int_(1)^(e )(f(x))/(x^(2))dx=(1)/(2) , then the value of int_(1)^(e ) f''(x)ln xdx equals :

If d/dx (ϕ(x))=f(x) , then int_(1)^(2) f(x) dx is ______

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Advanced (Archive)
  1. If int(n)=int(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,………. then

    Text Solution

    |

  2. Let f:[1,oo] be a differentiable function such that f(1)=2. If int1...

    Text Solution

    |

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

    Text Solution

    |

  4. int(1)^(e^(37))(pisin(pilogx))/(x)dx equals to.

    Text Solution

    |

  5. Prove that: int0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx

    Text Solution

    |

  6. The value of int2^3(sqrt(x))/(sqrt(5-x)+sqrt(x))dxi s

    Text Solution

    |

  7. The value of overset(3pi//4)underset(pi//4)int (x)/(1+sin x) dx is equ...

    Text Solution

    |

  8. The value of int(-2)^2|1-x^2|dx is

    Text Solution

    |

  9. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

    Text Solution

    |

  10. Match the conditions // expression in Column I with statement in Colum...

    Text Solution

    |

  11. Match List I with List II and select the correct answer using the code...

    Text Solution

    |

  12. Evaluate: 5050(int0 1(1-x^(50))^(100)dx)/(int0 1(1-x^(50))^(101)dx)

    Text Solution

    |

  13. Evaluate: int0^pie^(|cosx|)(2s in(1/2cosx)+3cos(1/2cosx))sinxdxdot

    Text Solution

    |

  14. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|pi/3))dx

    Text Solution

    |

  15. Show that: int0^(pi//2)f(sin2x)sinxdx=sqrt(2)int0^(pi//4)f(cos2x)co...

    Text Solution

    |

  16. int(-pi)^(pi) ( e^(sin x ))/( e^(sinx) + e^(-sinx))dx is equal to

    Text Solution

    |

  17. Prove that int(0)^(1)tan^(-1)(1/(1-x+x^(2)))dx=2int(0)^(1)tan^(-1)xdx....

    Text Solution

    |

  18. Evaluate int(0)^(pi//4) log (1+tan theta)d theta

    Text Solution

    |

  19. about to only mathematics

    Text Solution

    |

  20. Evaluate int(-1//sqrt(3))^(1//sqrt(3)) (x^(4))/(1-x^(4)) "cos"^(-1)((2...

    Text Solution

    |