Home
Class 12
MATHS
the value of int(0)^([x]) dx (where , [....

the value of `int_(0)^([x]) dx` (where , [.] denotes the greatest integer function)

Text Solution

Verified by Experts

The correct Answer is:
`(4pi-3sqrt(3))/(8pi+3sqrt(3))`
Promotional Banner

Topper's Solved these Questions

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|10 Videos

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS|Exercise Exercise For Session 2|20 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

Similar Questions

Explore conceptually related problems

The value of int_(0)^(2)[x+[x+[x]]] dx (where, [.] denotes the greatest integer function )is equal to

The value of int_(0)^(2)[x^(2)-x+1] dx (where , [.] denotes the greatest integer function ) is equal to

The value of int_(0)^(infty)[2e^(-x)] dx (where ,[.] denotes the greatest integer function of x) is equal to

The value of int_(0)^(10pi)[tan^(-1)x]dx (where, [.] denotes the greatest integer functionof x) is equal to

The value of lim_(xto0)(sin[x])/([x]) (where [.] denotes the greatest integer function) is

Evaluate int_0^a[x^n]dx, (where,[*] denotes the greatest integer function).

The value of int_(0)^(1000) e^(x - [x]) dx (where [.] is the greatest integer function) equals

The value of int_(-1)^(3){|x-2|+[x]} dx , where [.] denotes the greatest integer function, is equal to

The value of int_(1)^(10pi)([sec^(-1)x]) dx (where ,[.] denotes the greatest integer function ) is equal to

The value of int_(1)^(4){x}^([x]) dx (where , [.] and {.} denotes the greatest integer and fractional part of x) is equal to

ARIHANT MATHS-AREA OF BOUNDED REGIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. the value of int(0)^([x]) dx (where , [.] denotes the greatest integer...

    Text Solution

    |

  2. Area of the region {(x,y) in R^(2):ygesqrt(|x+3|),5ylex+9le15} is eq...

    Text Solution

    |

  3. Let F(x)=int(x)^(x^2+pi/2) 2 cos^(2)dt for all x in R and f:[0,1/2] to...

    Text Solution

    |

  4. The common tangents to the circle x^2=y^2=2 and the parabola y^(2)=8x ...

    Text Solution

    |

  5. The area enclosed by the curve y=sinx+cosxa n dy=|cosx-sinx| over the ...

    Text Solution

    |

  6. In Δ PQR, right-angled at Q, PR + QR = 30 cm and PQ = 10 cm. Determine...

    Text Solution

    |

  7. Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)for...

    Text Solution

    |

  8. Let the straight line x= b divide the area enclosed by y=(1-x)^(2),y=0...

    Text Solution

    |

  9. The area of the region bounded by the curve y=e^x and lines x=0a n dy=...

    Text Solution

    |

  10. The area of the region bounded by the curves y=sqrt[[1+sinx]/cosx] and...

    Text Solution

    |

  11. Find the product of (x - 4)(x - 7)

    Text Solution

    |

  12. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

    Text Solution

    |

  13. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

    Text Solution

    |

  14. The area (in sqaure units) of the region {(x,y):x ge 0, x + y le 3, x^...

    Text Solution

    |

  15. The area (in sq. units) of the region {(x,y):y^(2)ge2x and x^(2)+y^(2)...

    Text Solution

    |

  16. The area (in sq units) of the region described by {(x,y):y^(2)le2x and...

    Text Solution

    |

  17. The area (in sq. units) of the quadrilateral formed by the tangents ...

    Text Solution

    |

  18. The area of the region described by A={(x,y):x^(2)+y^(2)le1 and y^(2)l...

    Text Solution

    |

  19. The area bounded by the curves y=sqrt(x),2y+3=x , and x-axis in the 1s...

    Text Solution

    |

  20. The area bounded between the parabolas x^(2)=(y)/(4) and x^(2)=9y and ...

    Text Solution

    |

  21. The area of the region enclosed by the curves y=x, x=e,y=(1)/(x) and t...

    Text Solution

    |