Home
Class 12
MATHS
Ifint0^1(e^t dt)/(t+1)=a ,t h e ne v a l...

`Ifint_0^1(e^t dt)/(t+1)=a ,t h e ne v a l u a t eint_(b-1)^b(e^(-t)dt)/(t-b-1)`

A

`ae^(-b)`

B

`-ae^(-b)`

C

`-be^(-a)`

D

`ae^(b)`

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 int_0^1 (e^t dt)/(t+1)=a, then evaluate int_(b-1)^b (e^t dt)/(t-b-1)

If int1/(x+x^5)dx=f(x)+c ,t h e ne v a l u a t eint(x^4)/(x+x^5)dxdot

If int_0^1e^t/(t+1) dt=a , then int_(b-1)^b e^(-t)/(t-b-1) dt =

If int_0^1(e^t)/(1+t)dt=a , then find the value of int_0^1(e^t)/((1+t)^2)dt in terms of a .

int e^t sint dt

E v a l u a t e:int(x^4+x^2+1)/(x^2-x+1)dxdot

Let A=int_0^1(e^t)/(t+1)dt , then the value of (int_0^1t e^t^2)/(t^2+1)dt A^2 (b) 1/2A (c) 2A (d) 1/2A^2

Ifint_(pi/3)^xsqrt((3-sin^2t))dt+int_0^ycostdt=0,t h e ne v a l u a t e(dy)/(dx)

int(1)/(sqrt(t))dt

Evaluate int_(-oo)^(0)(te^(t))/(sqrt(1-e^(2t)))dt

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -Level - 1
  1. Let d/(dx)F(x)=(e^(sinx))/x . x lt0. If int(1)^(4)(2e^(sinx^(2)))/xdx=...

    Text Solution

    |

  2. Evaluate: int0^x[cost]dt where x in (2npi,(4n+1pi/2),n in N ,a n d[do...

    Text Solution

    |

  3. Ifint0^1(e^t dt)/(t+1)=a ,t h e ne v a l u a t eint(b-1)^b(e^(-t)dt)/(...

    Text Solution

    |

  4. The value of int0^pi (sin(n+1/2)x)/(sin (x/2)) dx is, (a) n in I, n >...

    Text Solution

    |

  5. Consider the integrals I(1)=overset(1)underset(0)inte^(-x)cos^(2)xdx...

    Text Solution

    |

  6. Given overset(2)underset(1)inte^(x^(2))dx=a, the value of overset(e^(4...

    Text Solution

    |

  7. The area bounded by the curve y=[x^2/64+2],y=x-1,y=x-1 and x=0 above t...

    Text Solution

    |

  8. Area enclosed by the curve (y-sin^(- 1)x)^2=x-x^2, is (A) pi/2 sq...

    Text Solution

    |

  9. Area of the region which consists of all the points satisfying the con...

    Text Solution

    |

  10. A point P(x,y) moves such that [x+y+1]=[x]. Where [.] denotes greatest...

    Text Solution

    |

  11. Two lines drawn through the point P (4, 0) divide the area bounded by ...

    Text Solution

    |

  12. The area of the smaller region in which the curve y=[(x^(3))/(100)+(x...

    Text Solution

    |

  13. Consider a rectangle ABCD formed by the points A=(0,0), B= (6, 0), C =...

    Text Solution

    |

  14. If f'(x) = f(x)+ int (0)^(1)f (x) dx and given f (0) =1, then int f (x...

    Text Solution

    |

  15. (sin 2 kx)/(sin x)=2[cos x + cos 3 x + …+cos (2k -1)x], then value of ...

    Text Solution

    |

  16. If int0^1(sint)/(1+t)dt=alpha, then the value of the integral int(4pi-...

    Text Solution

    |

  17. If n gt 1. Evaluate underset(0)overset(oo)int(dx)/((x+sqrt(1+x^(2)))^(...

    Text Solution

    |

  18. Let f(x) and g(x) be two functions satisfying f(x^(2))+g(4-x)=4x^(3),...

    Text Solution

    |

  19. f,g,h are continuous in [0,1],f(a-x)=f(x),g(a-x)=-g(x),3h(x)-4h(a-x)=5...

    Text Solution

    |

  20. The value of int(1)^(e)((tan^(-1))/x+(logx)/(1+x^(2)))dx is

    Text Solution

    |