Home
Class 12
MATHS
int(0)^(2)(x-[x])dx, where [x] is the gr...

`int_(0)^(2)(x-[x])dx`, where [x] is the greatest integer of x.

Text Solution

Verified by Experts

The correct Answer is:
1
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    ARIHANT PUBLICATION|Exercise PART V (QUESTIONS FOR PRACTICE) (6 MARK)|8 Videos

  • INTEGRATION

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (1 MARK)|26 Videos

  • INTEGRATION

    ARIHANT PUBLICATION|Exercise PART V (QUESTIONS FOR PRACTICE) (1 MARK)|25 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (LONG ANSWER TYPE QUESTIONS)|21 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE |35 Videos

Similar Questions

Explore conceptually related problems

int_0^(3/2)[2x]dx

Write the value of int_(0)^(1)[x]dx , where [x] stands for fractional part of x.

If f f(x)=cos[pi^2]x+cos[-pi^2]x where [x] stands for the greatest integer functions, then evaluate f(pi/2),f(pi),f(-pi), andf(pi/4) .

Prove that the greatest integer function f:R rarr R, given by f(x) = [x] is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

int_0^1(dx)/(3x+2)

int_1/((x+1)(x+2))dx

int_(-2)^1((abs(x))+x)dx

I=int_0^4(x^2+2x+4)dx

ARIHANT PUBLICATION-INTEGRATION -PART V (QUESTIONS FOR PRACTICE) (4 MARK)
  1. Evaluate the following integrals : int(pi//3)^(pi//2)(sqrt((1+cosx))...

    Text Solution

    |

  2. Evaluate the following integrals : int(0)^(pi//4)(dx)/(cos^(3)xsqrt(...

    Text Solution

    |

  3. Evaluate the following integrals : int(0)^(1//sqrt(2))(sin^(-1)x)/((...

    Text Solution

    |

  4. Evaluate the following integrals : int(tan^(-1)x) dx.

    Text Solution

    |

  5. Evaluate the following integrals : int(0)^(1)x^(5)(4-x^(2))dx.

    Text Solution

    |

  6. Evaluate the following integrals : int(0)^(1)x^(7)sqrt((1+x^(2))/(1-...

    Text Solution

    |

  7. Evaluate the following integrals : int(0)^(a)x^(2)(a^(2)-x^(2))dx

    Text Solution

    |

  8. If f is an even function and int(-2)^(0)f(t)dt=(3)/(2), then find int(...

    Text Solution

    |

  9. int(0)^(2)(x-[x])dx, where [x] is the greatest integer of x.

    Text Solution

    |

  10. Evaluate the following integrals : int(-1)^(2){|x|+[x]}dx

    Text Solution

    |

  11. Evaluate the following integrals : int(0)^(1)2x(1-x)^(n)dx.

    Text Solution

    |

  12. Evaluate the following integrals : int(0)^(2)xsqrt(2-x)dx.

    Text Solution

    |

  13. Evaluate the following integrals : int(0)^(pi//2)(tan^(7)x)/(cot^(7)...

    Text Solution

    |

  14. Evaluate the following integrals : int(0)^(pi//2)(dx)/(1+sqrt(tanx))

    Text Solution

    |

  15. Evaluate the following integrals : int(0)^(pi//2)log|(4+3sinx)/(4+3c...

    Text Solution

    |

  16. Evaluate the following integrals : int(0)^(1)log|(1)/(x)-1|dx.

    Text Solution

    |

  17. Evaluate the following integrals : int(0)^(pi//2)(sinx-cosx)/(1+sinx...

    Text Solution

    |

  18. Evaluate the following integrals : int(0)^(1)tan^(-1)((2x-1)/(1+x-x^...

    Text Solution

    |

  19. Evaluate the following integrals : int(0)^(1)cot^(-1){1-x+x^(2)}dx.

    Text Solution

    |

  20. Show that int(0)^(pi)log|tanx|dx=0.

    Text Solution

    |