Home
Class 12
MATHS
Let f(x)=x-[x], for ever real numb...

Let `f(x)=x-[x],` for ever real number `x ,w h e r e[x]` is the greatest integer less than or equal to `xdot` Then, evaluate `int_(-1)^1f(x)dx` .

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    RD SHARMA ENGLISH|Exercise All Questions|282 Videos

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA ENGLISH|Exercise All Questions|168 Videos

Similar Questions

Explore conceptually related problems

If f(x)=|x-1|-[x] , where [x] is the greatest integer less than or equal to x, then

Let [x] denote the greatest integer less than or equal to x . Then, int_(0)^(1.5)[x]dx=?

If f(x)=|x|+[x] , where [x] is the greatest integer less than or equal to x, the value of f(-2.5)+f(1.5) is

Let [x] denotes the greatest integer less than or equal to x and f(x)=[tan^(2)x] . Then

If f(x)=cos[pi]^2x+cos[-pi^2]x ,\ w h e r e\ [x] denotes the greatest integer less than or equal to x , then write the value of f(pi)dot

Let f(x)=max. {x+|x|,x-[x]} , where [x] denotes the greatest integer less than or equal to x, then int_(-2)^(2) f(x) is equal to

Let f(x) = x-[x] , for every real number x, where [x] is integral part of x. Then int_(-1) ^1 f(x) dx is

Let f(x) be defined by f(x) = x- [x], 0!=x in R , where [x] is the greatest integer less than or equal to x then the number of solutions of f(x) +f(1/x) =1

Let f(x) be defined by f(x) = x- [x], 0!=x in R , where [x] is the greatest integer less than or equal to x then the number of solutions of f(x) +f(1/x) =1

Let [x] denotes the greatest integer less than or equal to x. If f(x) =[x sin pi x] , then f(x) is

RD SHARMA ENGLISH-DEFINITE INTEGRALS-All Questions
  1. Evaluate the following definite integrals (1-58): int1^2 1/(sqrt((x...

    Text Solution

    |

  2. Evaluate the following integrals: int0^picosx|cosx|dx

    Text Solution

    |

  3. Let f(x)=x-[x], for ever real number x ,w h e r e[x] is the g...

    Text Solution

    |

  4. Evaluate: int0^(sqrt(3))1/(1+x^2)sin^(-1)((2x)/(1+x^2))dx

    Text Solution

    |

  5. Evaluate the following integrals: int0^9f(x)dx ,w h e r ef(x)={si...

    Text Solution

    |

  6. Evaluate the following integrals: int0^2|x^2-3x+2|dx

    Text Solution

    |

  7. Evaluate the following integrals: int0^1sqrt((1-x)/(1+x))dx

    Text Solution

    |

  8. Prove that: inta^b(f(x))/(f(x)+f(a+b-x))dx=(b-a)/2

    Text Solution

    |

  9. Evaluate of each of the following integrals (1-15): int0^5(root(3)(x...

    Text Solution

    |

  10. Evaluate of each of the following integrals (1-15): int(-pi//4)^(p...

    Text Solution

    |

  11. Evaluate of each of the following integrals (1-15): int(-a)^a1/(1+"...

    Text Solution

    |

  12. Evalaute int(pi//6)^(pi//3)(sqrt((sinx))dx)/(sqrt((sinx))+sqrt((cosx))...

    Text Solution

    |

  13. Evaluate of each of the following integrals (1-15): int0^(2pi)"log...

    Text Solution

    |

  14. Evaluate: int(-pi//4)^(pi//4)(sec^2x)/(1+e^x)dx

    Text Solution

    |

  15. Evaluate: int(-pi//4)^(pi//4)(sec^2x)/(1+e^x)dx

    Text Solution

    |

  16. Evaluate: int(-pi//2)^(pi//2)(xsinx)/(e^x+1)dx

    Text Solution

    |

  17. If f(a+b-x)=f(x), then prove that inta^b xf(x)dx=(a+b)/2inta^bf...

    Text Solution

    |

  18. Evaluate of each of the following integrals (1-15): int0^7(x^(1/3)...

    Text Solution

    |

  19. Evaluate: int1^2x^2dx

    Text Solution

    |

  20. Evaluate: int(4)^(1)1/x dx

    Text Solution

    |