Home
Class 12
MATHS
Let f:RtoR be a function defined by f(x)...

Let `f:RtoR` be a function defined by `f(x)={([x],xle2),(0,xgt2):}` where `[x]` is th greatest integer less than or equal to `x`. If `I=int_(-1)^(2)(xf(x^(2)))/(2+f(x+1))dx`, then the value of `(4I-1)` is

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|5 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

  • DETERMINANTS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

Let f: RvecR be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) where [x] is the greatest integer less than or equal to xdot If I=int_(-1)^2(xf(x^2))/(2+f(x+1))dx , then \ the \ value \ of \ (4I-1)i s

The function f(x)=(tan |pi[x-pi]|)/(1+[x]^(2)) , where [x] denotes the greatest integer less than or equal to x, is

The domain of the function f(x)=cos^(-1)[secx] , where [x] denotes the greatest integer less than or equal to x, is

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

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 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

The domain of the function f(x) = sqrt((4-x^(2))/([x]+2)) where [x] denotes the greatest integer less than or equal to x,is

If the function f: R->R be such that f(x) = x-[x], where [x] denotes the greatest integer less than or equal to x, then f^-1(x) is

If f(x)=inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx,f(0)=0 then the value of f(1) is

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 .

ARIHANT MATHS ENGLISH-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  2. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  3. Let f:RtoR be a function defined by f(x)={([x],xle2),(0,xgt2):} where ...

    Text Solution

    |

  4. If alpha=int0^1(e^(9x+3tan^((-1)x)))((12+9x^2)/(1+x^2))dxw h e r etan^...

    Text Solution

    |

  5. The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equ...

    Text Solution

    |

  6. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  7. Match the conditions/ expressions in Column I with statement in Column...

    Text Solution

    |

  8. Match List I with List II and select the correct answer using codes gi...

    Text Solution

    |

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

    Text Solution

    |

  10. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

    Text Solution

    |

  11. The valued of int(sqrt(In2))^(sqrt(In3)) (x sinx^(2))/(sinx^(2)+sin(In...

    Text Solution

    |

  12. Let f:[1,oo] be a differentiable function such that f(1)=2. If int1...

    Text Solution

    |

  13. The value of int(0)^(1)(x^(4)(1-x)^(4))/(1+x^(4))dx is (are)

    Text Solution

    |

  14. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

    Text Solution

    |

  15. Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...

    Text Solution

    |

  16. Which of the following is true?

    Text Solution

    |

  17. For any real number x ,l e t[x] denote the largest integer less than o...

    Text Solution

    |

  18. Let f be a non-negative function defined on the interval [0,1]. If int...

    Text Solution

    |

  19. If int(n)=int(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,………. then

    Text Solution

    |

  20. Let S(n)=sum(k=1)^(n)n/(n^(2)+kn+k^(2)) and T(n)=sum(k=0)^(n-1)n/(n^(2...

    Text Solution

    |