Home
Class 12
MATHS
The value of int(0)^(2)xd([x]-x), is...

The value of `int_(0)^(2)xd([x]-x)`, is

A

`1//2`

B

1

C

`-1`

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
Using partial integration, formula, we obtain
`underset(0)overset(2)intxd([x]-x)`
`[x([x]-x)]_(0)^(2)-underset(0)overset(2)int([x]-x)dx`
`=2(2-2)-0-underset(0)overset(2)int([x]-x)dx`
`[underset(0)overset(1)int(0-x)dx+underset(1)overset(2)int(1-x)dx]`
`=-[[(x^(2))/(2)]_(0)^(1)+[x-(x^(2))/(2)]_(1)^(2)]`
`=-[(-(1)/(2)+0)+(2-2)=-(1-(1)/(2))]=1`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|145 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|12 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA|Exercise Exercise|86 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

The value of int_(0)^(2)|1-x|dx

Let f(x) be a differentiable function in the interval (0,2) then the value of int_(0)^(2)f(x) is

For any real number x,the value of int_(0)^(x)[x]dx is

The value of int_(0)^(1)x^(2)e^(x)dx is equal to

The value of int_(0)^(2)xe^(x^(2))dx

The value of int_(0)^(1)x|x-1/2|dx is

If f(x)=max{x^(2),(1-x)^(2),(3)/(4)},x in[0,1] then the value of of int_(0)^(1)f(x)dx is

The value of int_(0)^(2)((x^(2)-2x+4)sin(x-1))/(2x^(2)-4x+5)dx is equal to

The value of int_(0)^(pi//2) x^(10) sin x" dx" , is then the value of mu_(10)+90mu_(8) , is

OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 2
  1. The value of int(0)^(2)xd([x]-x), is

    Text Solution

    |

  2. The integral int(0)^(r pi) sin^(2x)x dx is equal to

    Text Solution

    |

  3. The value of the integral int(0)^(2)x[x]dx

    Text Solution

    |

  4. The value of integral sum (k=1)^(n) int (0)^(1) f(k - 1+x) dx is

    Text Solution

    |

  5. Let f(x) be a funntion satifying f'(x)=f(x) with f(0)=1 and g(x) be th...

    Text Solution

    |

  6. If I=int(0)^(1) cos{ 2 "cot"^(-1)sqrt((1-x)/(1+x))}dx then

    Text Solution

    |

  7. The value of int(a)^(a+(pi//2))(sin^(4)x+cos^(4)x)dx is

    Text Solution

    |

  8. The vaue of int(-1)^(2) (|x|)/(x)dx is

    Text Solution

    |

  9. The value of int0^1 (x^(3))/(1+x^(8))dx is

    Text Solution

    |

  10. The value of int(0)^(3) xsqrt(1+x)dx, is

    Text Solution

    |

  11. The value of the integral int(0)^(1) log sin ((pix)/(2))dx is

    Text Solution

    |

  12. The value of the integral int(0)^(pi)x log sin x dx is

    Text Solution

    |

  13. If I(1)=int(0)^(oo) (dx)/(1+x^(4))dx and I(2)underset(0)overset(oo)in...

    Text Solution

    |

  14. If f(x)={{:(x,"for " x lt 1),(x-1,"for " x ge1):},"then" int(0)^(2) x...

    Text Solution

    |

  15. The value of the integral int(0)^(2) (1)/((x^(2)+1)^(3//2))dx is

    Text Solution

    |

  16. If int(0)^(2a) f(x)dx=int(0)^(2a) f(x)dx, then

    Text Solution

    |

  17. If int(0)^(36) (1)/(2x+9)dx =log k, is equal to

    Text Solution

    |

  18. The value of the integral int(0)^(pi//2) sin^(6) x dx, is

    Text Solution

    |

  19. If int(0)^(oo) e^(-x^(2))dx=sqrt((pi)/(2))"then"int(0)^(oo) e^(-ax^(2)...

    Text Solution

    |

  20. The value of the integral int 0^oo 1/(1+x^4)dx is

    Text Solution

    |

  21. If int(pi//2)^(x) sqrt(3-2sin^(2)u) dx+int(dx)^(dy) equal pi//2

    Text Solution

    |