Home
Class 12
MATHS
If [dot]a n d\ {dot} denote respectively...

If `[dot]a n d\ {dot}` denote respectively the greatest integer and fractional part functional respectively, evaluate the following integral: `int_0^(sqrt(2))[x^2]dx`

Text Solution

Verified by Experts

` \begin{array}{l} I=\int_{0}^{\sqrt{2}}[x^{2}] d x \\ x=0 ; x=\sqrt{2}[x^{2}] \\ 0
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    RD SHARMA|Exercise Solved Examples And Exercises|277 Videos

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

If [dot]a n d\ {dot} denote respectively the greatest integer and fractional part functional respectively, evaluate the following integral: int_0^2[x]dx

If [dot]a n d\ {dot} denote respectively the greatest integer and fractional part functional respectively, evaluate the following integral: int_0^1{x}dx

If [dot]a n d\ {dot} denote respectively the greatest integer and fractional part functional respectively, evaluate the following integral: int_0^2x[x]dx

If [dot]a n d\ {dot} denote respectively the greatest integer and fractional part functional respectively, evaluate the following integral: int_0^(15)[x]dx

If [dot]a n d\ {dot} denote respectively the greatest integer and fractional part functional respectively, evaluate the following integral: int_0^1e^([x])dx

If [dot]a n d\ {dot} denote respectively the greatest integer and fractional part functional respectively, evaluate the following integral: int_0^1 2^(x-[x])dx

If [dot]a n d\ {dot} denote respectively the greatest integer and fractional part functional respectively, evaluate the following integral: int_1^2(log)_e\ \ [x]dx

If f(x)=[x^(2)]+sqrt({x}^(2)), where [] and {.} denote the greatest integer and fractional part functions respectively,then

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

RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

    Text Solution

    |

  2. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

    Text Solution

    |

  3. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

    Text Solution

    |

  4. The value of int0^(pi//2)(sqrt(cosx))/(sqrt(cos x)+sqrt(s in x))dx is ...

    Text Solution

    |

  5. int0^(pi/2) 1/(1+sinx)dx equals 0 b. 1//2 c. 2 d. 3//2

    Text Solution

    |

  6. int0^oo1/(1+e^x)dx equals a. log2-1 b. log2 c. log4-1 d. log2

    Text Solution

    |

  7. The value of int0^(2pi)sqrt(1+sin (x/2)dx is 0 b. 4 c. 2 d. 8

    Text Solution

    |

  8. int0^(pi^2//4)(sinsqrt(x))/(sqrt(x))dx equals a. pi^2//8 b. pi//4 ...

    Text Solution

    |

  9. int0^(pi//2)1/(2+cos\ x)dx equals 1/3tan^(-1)(1/(sqrt(3))) b. 2/(sqrt(...

    Text Solution

    |

  10. 36/piint(pi//6)^(pi//3)(dx)/(1+sqrt(cotx)) equals to

    Text Solution

    |

  11. Given that int0^oo(x^2)/((x^2+a^2)(x^2+b^2)(x^2+c^2))dx=pi/(2(a+b)(b+c...

    Text Solution

    |

  12. int1^elogx\ dx= 1 b. e-1 c. e+1 d. 0

    Text Solution

    |

  13. int1^(sqrt(3))1/(1+x^2)dx is equal to pi/(12) b. pi/4 c. pi/6 d. pi/3

    Text Solution

    |

  14. The value of int0^(pi//2)cosx\ e^(sin x)dx\ i s 1 b. e-1 c. 0 d. -1

    Text Solution

    |

  15. If int0^a1/(1+4x^2)dx=\ pi/8 , then a equals pi/2 b. pi/4 c. 1/2 d. 1

    Text Solution

    |

  16. int0^1f(x)dx=1,\ int0^1xf(x)dx=a ,\ int0^1x^2f(x)dx=a^2,\ t h e n\ int...

    Text Solution

    |

  17. The value of int(-pi)^pisin^3xcos^2x\ dx\ is (pi^4)/2 b. (pi^4)/4 c. ...

    Text Solution

    |

  18. int(pi//6)^(pi//3)1/(sin2x)dx\ is equal to (log)e3 b. (log)"e"sqrt(3...

    Text Solution

    |

  19. int(-1)^1|1-x|dx is equal to -2 b. 2 c. 0 d. 4

    Text Solution

    |

  20. (lim)(n->oo){1/(2n+1)+1/(2n+2)++1/(2n+n)} I n\ (1/3) b. I n\ (2/3) c....

    Text Solution

    |