Home
Class 12
MATHS
Consider the integral I=int(0)^(10)([x]e...

Consider the integral `I=int_(0)^(10)([x]e^([x]))/(e^(x-1))dx`, where [x] denotes the greatest integer less than or equal to x. Then the value of I is equal to :

A

45 (e-1)

B

45(e+1)

C

9(e+1)

D

(e-1)

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN 2021

    JEE MAINS PREVIOUS YEAR|Exercise Mathematic section B|10 Videos

  • JEE MAIN 2021

    JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS SECTION B|20 Videos

  • JEE MAIN

    JEE MAINS PREVIOUS YEAR|Exercise QUESTION|1 Videos

  • JEE MAIN 2022

    JEE MAINS PREVIOUS YEAR|Exercise Question|454 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(15/2)[x-1]dx= where [x] denotes the greatest integer less than or equal to x

If [x] denotes the greatest integer less than or equal to x then the value of int_(0)^(2)(|x-2|+[x])dx is equal to

Let f(x)=(x-[x])/(1+x-[x]), where [x] denotes the greatest integer less than or equal to x,then the range of f is

Let [x] denote the greatest integer less than or equal to x. Then the value of int_(1)^(2)|2x-[3x]|dx is ______

lim_(xrarr oo) (log[x])/(x) , where [x] denotes the greatest integer less than or equal to x, is

Let [x] denote the greatest integer less than or equal to x, then the value of the integral int_(-1)^(1)(|x|-2[x])dx is equal to

If I=int_(-1)^(1) {[x^(2)]+log((2+x)/(2-x))}dx where [x] denotes the greatest integer less than or equal to x, the I equals

If [x] dentoes the greatest integer less than or equal to x, then the value of int _(0)^(5)[|x-3|] dx is

int_(0)^([x]//3) (8^(x))/(2^([3x]))dx where [.] denotes the greatest integer function, is equal to

JEE MAINS PREVIOUS YEAR-JEE MAIN 2021-Mathematic section A
  1. Let C be the locus of the mirror image of a point on the parabola y^(2...

    Text Solution

    |

  2. Let veca=hati+2hatj-3hatk and vecb=2hati-3hatj+5hatk. If vecrxxveca=ve...

    Text Solution

    |

  3. Let (x,y,z) be an arbitrary point lying on a plane P which passes thro...

    Text Solution

    |

  4. Let f be a real valued function, defined on R-{-1, 1} and given by f(x...

    Text Solution

    |

  5. Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4,...

    Text Solution

    |

  6. Let C, be the curve obtained by the solution of differential equation ...

    Text Solution

    |

  7. The least value of |z| where z is complex number which satisfies the i...

    Text Solution

    |

  8. Let C(1) be the curve obtained by the solution of differential equatio...

    Text Solution

    |

  9. Let A(-1, 1), B(3, 4) and C(2,0) be given three points. A line y=mx,mg...

    Text Solution

    |

  10. Let f:StoS where S=(0,oo) be a twice differentiable function such that...

    Text Solution

    |

  11. Let the lengths of intercepts on x-axis and y-axis made by the circle ...

    Text Solution

    |

  12. Given that the inverse trigonometric functions take principal values o...

    Text Solution

    |

  13. If the foot of the perpendicular from point (4, 3,8) on the line L(1):...

    Text Solution

    |

  14. Let A = (1,2, 3, 4, 5, ..., 30) and ~=be an equivalence relation on Ax...

    Text Solution

    |

  15. Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of ...

    Text Solution

    |

  16. Let P(x)=x^(2)+bx+c be a quadratic polynomial with real coefficients s...

    Text Solution

    |

  17. Consider the integral I=int(0)^(10)([x]e^([x]))/(e^(x-1))dx, where [x]...

    Text Solution

    |

  18. Let alphainR be such that the function f(x)={{:((cos^(-1)(1-{x}^(2))si...

    Text Solution

    |

  19. The maximum value of f(x)=|(sin^(2)x,1+cos^(2)x,cos2x),(1+sin^(2)x,cos...

    Text Solution

    |

  20. If the points of intersections of the ellipse (x^(2))/(16)+(y^(2))/(b^...

    Text Solution

    |