Home
Class 12
MATHS
Let d/(dx) (F(x))= e^(sinx)/x, x>0. If ...

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:

Text Solution

Verified by Experts

`I=int_(1)^(4)(2e^(sinx^(2)))/xdx=F(k)-F(1)=[F(x)]_(1)^(k)`
Now put `x^(2)=t`
`:.2xdx=dt`
`:.I=int_(1)^(16)(e^(sint))/tdt=[F(t)]_(1)^(16)`
`:.I=F(16)-F(1)`
`=:.k=16`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.1|4 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.2|17 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

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

Let (d)/(dx)F(x)=((e^( sin x))/(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(cc)63 (d) 64

int[(d)/(dx)f(x)]dx=

Let f:[2,5] rarr [2,5] be a bijective function such that d/(dx)f^-1(x)>0AA(x)in[2, 5] then int_2^5(f(x)+f^-1(x)) s dx is equal to 7k. then value of k is

if (d)/(dx)f(x)=g(x), find the value of int_(a)^(b)f(x)g(x)dx

CENGAGE-DEFINITE INTEGRATION -JEE Advanced Previous Year
  1. Let d/(dx) (F(x))= e^(sinx)/x, x>0. If int1^4 2e^sin(x^2)/x dx = F(k)...

    Text Solution

    |

  2. Let f be a non-negative function defined on the interval .[0,1].If int...

    Text Solution

    |

  3. The value of int0^1(x^4(1-x)^4)/(1+x^2)\ dx is

    Text Solution

    |

  4. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  5. The valued of int(sqrt(In2))^(sqrt(In3)) (x sinx^(2))/(sinx^(2)+sin(In...

    Text Solution

    |

  6. Let f:[-1,2]vec[0,oo) be a continuous function such that f(x)=f(1-x)fo...

    Text Solution

    |

  7. Let f:[1/2,1]vecR (the set of all real numbers) be a positive, non-con...

    Text Solution

    |

  8. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  9. int((pi)/4)^((pi)/2)(2cosecx)^17 dx

    Text Solution

    |

  10. Let f prime(x)=(192x^3)/(2+sin^4 pix) for all x in RR with f(1/2)=0. I...

    Text Solution

    |

  11. Evaluate: int(-pi//2)^(pi//2)(cosx)/(1+e^x)dx

    Text Solution

    |

  12. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

    Text Solution

    |

  13. Let f be a real-valued function defined on interval (0,oo),by f(x)=lnx...

    Text Solution

    |

  14. Let S be the area of the region enclosed by y=e^-x^2,y=0,x=0,a n dx=1....

    Text Solution

    |

  15. Find a for which lim(n->oo) (1^a+2^a+3^a+...+n^a)/((n+1)^(a-1)[(na+1)+...

    Text Solution

    |

  16. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

    Text Solution

    |

  17. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^-(t+(1...

    Text Solution

    |

  18. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  19. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^4x-3tan^2x for all x in (-pi/2,...

    Text Solution

    |

  20. Let f(x)=lim(n->oo)((n^n(x+n)(x+n/2)....(x+n/n))/(n!(x^2+n^2)(x^2+n^2/...

    Text Solution

    |

  21. Let f: Rvec(0,1) be a continuous function. Then, which of the followin...

    Text Solution

    |