Home
Class 12
MATHS
Find the value of int(-1)^(1)[x^(2)+{x}]...

Find the value of `int_(-1)^(1)[x^(2)+{x}]dx`, where [.] and `{.}` denote the greatest function and fractional parts of `x`, respectiely.

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

Find the value of int_(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot} denote the greatest function and fractional parts of x , respectively.

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

f(x)=[x^(2)]-{x}^(2), where [.] and {.} denote the greatest integer function and the fractional part function , respectively , is

Solve 2[x]=x+{x},where [.] and {} denote the greatest integer function and the fractional part function, respectively.

Solve : [x]^(2)=x+2{x}, where [.] and {.} denote the greatest integer and the fractional part functions, respectively.

Solve the equation [x]{x}=x, where [] and {} denote the greatest integer function and fractional part, respectively.

The value of int_(0)^(2)[x^(2)-1]dx , where [x] denotes the greatest integer function, is given by:

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

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

The value of I = int_(-1)^(1)[x sin(pix)]dx is (where [.] denotes the greatest integer function)

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. Evaluate: int1^(e^6)[(logx)/3]dx ,w h e r e[dot] denotes the greatest...

    Text Solution

    |

  2. If int(0)^(oo) (sinx)/x dx=(pi)/2, then int(0)^(oo) (sin^(3)x)/x dx i...

    Text Solution

    |

  3. Find the value of int(-1)^(1)[x^(2)+{x}]dx, where [.] and {.} denote t...

    Text Solution

    |

  4. int0^x[cost]dt ,w h e r ex in (2npi,2npi+pi/2),n in N ,a n d[dot] de...

    Text Solution

    |

  5. Evaluate: int(-pi/2)^(2pi)[cot^(-1)x]dx , where [dot] denotes the grea...

    Text Solution

    |

  6. Evaluate: int(-pi/2)^(2pi)[cot^(-1)x]dx , where [dot] denotes the grea...

    Text Solution

    |

  7. f(x) is continuous function for all real values of x and satisfies int...

    Text Solution

    |

  8. Prove that int0^1xe^xdx=1

    Text Solution

    |

  9. I1=int0^(pi/2)ln(sinx)dx ,I2=int(-pi/4)^(pi/4)ln(sinx+cosx)dxdot Then ...

    Text Solution

    |

  10. Prove that int0^oo[n e^(-x)]dx=ln((n^n)/(n !)),w h e r en is a na...

    Text Solution

    |

  11. For x in R and a continuous function f, let I1=int(sin^2t)^(1+cos^2t)...

    Text Solution

    |

  12. Evaluate of each of the following integrals int(pi//6)^(pi//3)(sqrt...

    Text Solution

    |

  13. Given a function f:[0,4]toR is differentiable ,then prove that for som...

    Text Solution

    |

  14. Evaluate: int0^(pi/2)log((4+3sinx)/(4+3cosx))dx

    Text Solution

    |

  15. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx is

    Text Solution

    |

  16. Evaluate: int(-pi)^(3pi)log(s e c theta-t a ntheta)d theta

    Text Solution

    |

  17. The value of the integral overset(1)underset(0)int e^(x^(2))dx lies in...

    Text Solution

    |

  18. Let P(x) be a polynomial of least degree whose graph has three points ...

    Text Solution

    |

  19. IfIn=int0^1(dx)/((1+x^2)^n),w h e r en in N , which of the following...

    Text Solution

    |

  20. If f(0)=1,f(2)=3,f^'(2)=5,then find the value of int0^1xf^('')(2x)d...

    Text Solution

    |