Home
Class 12
MATHS
For any real number x, let [x] denote th...

For any real number `x`, let `[x]` denote the largest integer less than or equal to `x`, Let `f` be a real-valued function defined on the interval `[-10 , 10]` be `f(x)={x-[x], if [x]` is odd, `1+[x]-x ,if[x]` is even Then the value of `(pi^2)/(10)int_(-10)^(10)f(x)cospixdx` is____

Text Solution

Verified by Experts

The correct Answer is:
4
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 1|15 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 2|14 Videos

  • COORDINATE SYSTEM AND COORDINATES

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

  • DETERMINANTS

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

Similar Questions

Explore conceptually related problems

If f(x)=x-[x], where [x] is the greatest integer less than or equal to x, then f(+1/2) is:

Let [x] = the greatest integer less than or equal to x and let f (x) = sin x + cosx. Then the most general solution of f(x)=[f(pi/10)] 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 .

Let f be a real - valued function defined on R ( the set of real numbers) such that f(x) = sin^(-1) ( sin x) + cos^(-1) ( cos x) The value of f(10) is equal to

Let f be a real valued function defined on the interval (0,oo) by f(x)=In x+int_(0)^(x)sqrt(1+sint)dt . Then which of the following statement (s) is (are) true?

f(x)= 1/sqrt([x]-x) , where [*] denotes the greatest integeral function less than or equals to x. Then, find the domain of f(x).

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

Let f be a real-valued function defined on the inverval (-1,1) such that e^(-x)f(x)=2+int_0^xsqrt(t^4+1)dt , for all, x in (-1,1)and f^(-1) be the inverse function of fdot Then (f^(-1))^'(2) is equal to

The set A = {x : x is an odd number less than 10} equals :

If f(x)=sin{(pi)/(3)[x]-x^(2)}" for "2ltxlt3 and [x] denotes the greatest integer less than or equal to x, then f'"("sqrt(pi//3)")" is equal to

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
  1. For any real number x, let [x] denote the largest integer less than or...

    Text Solution

    |

  2. The total number of distinct x in R for which |{:(x,x^(2),1+x^(3)...

    Text Solution

    |

  3. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) . ...

    Text Solution

    |

  4. Let f'(x)=(192x^(3))/(2+sin^(4)pix) for all x epsilonR with f(1/2)=0. ...

    Text Solution

    |

  5. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  6. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  7. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

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

    Text Solution

    |

  9. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. Find x+y+z

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. The value of int(In2)^(In3) (x sinx)dx is

    Text Solution

    |

  17. Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int1...

    Text Solution

    |

  18. The value of int(0)^(1)(x^(4)(1-x)^(4))/(1+x^(2))dx is (are)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  21. Which of the following is true?

    Text Solution

    |