Home
Class 12
MATHS
The integral underset1overseteint{(x/e)^...

The integral `underset1overseteint{(x/e)^(2x)-(e/x)^x}log_exdx` is equal to

A

`(3)/(2)-(1)/(e )-(1)/(2e^(2))`

B

`(3)/(2)-e-(1)/(2e^(2))`

C

`-(1)/(2)+(1)/(e )-(1)/(2e^(2))`

D

`(1)/(2)-e-(1)/(e^(2))`

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 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

The integral int_(1)^(e){(x/e)^(2x)-(e/x)^x}log_exdx is equal to

intx^(x)(1+log_(e)x) dx is equal to

int_(1)^(3)|(2-x)log_(e )x|dx is equal to:

intsin2x*log_(e)cosxdx is equal to

The value of the integral underset(e^(-1))overset(e^(2))int |(log_(e)x)/(x)|dx is

The integral int(1+x-1/x)e^(x+1/x)dx is equal to

The value of int_(log1//2)^(log2)sin{(e^(x)-1)/(e^(x)+1)}dx is equal to

Integrate int(x*e^(x))/((1+x)^(2))dx .

The integral inte^x(f(x)+f\'(x))dx can be solved by using integration by parts such that: I=inte^xf(x)dx+inte^xf\'(x)dx=e^xf(x)-inte^xf\'(x)dx+inte^xf\'(x)dx=e^xf(x)+C , and inte^(ax)(f(x)+(f\'(x))/a)dx=e^(ax)f(x)/a+C ,Now answer the question: int{log_e(log_ex)+1/(log_ex)^2}dx is equal to (A) log_e(log_ex)+C (B) xlog_e(log_ex)-x/log_ex+C (C) x/log_ex-log_ex+C (D) log_e(log_ex)-x/log_ex+C

The value of the definite integral int e^(-x^4) (2+ln(x+sqrt(x^2+1))+5x^3-8x^4)dx is equal to

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Main (Archive)
  1. The area (in sq. units) of the region bounded by the parabola y=x^2+2"...

    Text Solution

    |

  2. Let f and g be continuous fuctions on [0, a] such that f(x)=f(a-x)" an...

    Text Solution

    |

  3. The integral underset1overseteint{(x/e)^(2x)-(e/x)^x}logexdx is equal ...

    Text Solution

    |

  4. The area (in sq. units) of the region A={(x,y)in R xx R |0 le x le 3, ...

    Text Solution

    |

  5. If f(x)=(2-xcosx)/(2+xcosx)andg(x)= "log"(e)x, (xgt0) then the value ...

    Text Solution

    |

  6. Let f ( x) = int 0 ^ x g (t) dt , where g is a non - ze...

    Text Solution

    |

  7. Let f(x,y) = {(x,y): y^(2) le 4x,0 le x le lambda} and s(lambda) is a...

    Text Solution

    |

  8. int(0)^((pi)/(2))(sin^(3)x)/(sinx+cosx)dx is equal to

    Text Solution

    |

  9. The area (in sq. units) of the region {(x,y) in R^(2) : x^(2) le y le ...

    Text Solution

    |

  10. The value of the integral int(0)^(1)xcot^(-1)(1-x^(2)+x^(4))dx is

    Text Solution

    |

  11. The area (in sq. units) of the region A = {(x,y), y^(2)//2 le x le y +...

    Text Solution

    |

  12. The value of int(0)^(2pi)[sin2x (1+cos 3x)]dx, where [t] denotes the g...

    Text Solution

    |

  13. The region represented by |x-y|le 2 and |x +y| le 2 is bounded by a:

    Text Solution

    |

  14. The integral int sec^(2//3)x cosec^(4//3)x dx is equal to : (Here ...

    Text Solution

    |

  15. The area (in sq. units) of the region bounded by the curves y=2^(x) an...

    Text Solution

    |

  16. If int(0)^(pi//2) (cot x)/(cot x+cosecx)dx=m(pi+n), then m*n is equal ...

    Text Solution

    |

  17. If the area (in sq. units) of the region {(x,y): y^(2) lt= 4x,x+y lt...

    Text Solution

    |

  18. Let f : R to R be a continuously differentiable function such that f(...

    Text Solution

    |

  19. A value of alpha such that int(alpha)^(alpha+1) (dx)/((x+a)(x+...

    Text Solution

    |

  20. If the area (in sq. units) bounded by the parabola y^(2)=4lamdax and t...

    Text Solution

    |