Home
Class 12
MATHS
It is known that f(x) is an odd function...

It is known that `f(x)` is an odd function in the interval `[p/2, p/2]` and has a period `p ,` Prove that `int_q^x(t)dt` is also periodic function with the same period.

A

a periodic function with period `T//2`

B

a periodic function with period T

C

not a periodic function

D

a periodic function with period`T//4`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test 1|57 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test 2|56 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|12 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

It is known that f(x) is an odd function in the interval [-p/2, p/2] and has a period p , Prove that int_a^xf(t)dt is also periodic function with the same period.

It is known that f(x) is an odd function and has a period p . Prove that int_(a)^(x)f(t)dt is also periodic function with the same period.

If f(x) is periodic function with period, T, then

Prove that f(x)=x-[x] is periodic function. Also, find its period.

If f(x+10) + f(x+4)= 0 , there f(x) is a periodic function with period

If f(x) is an odd periodic function with period 2, then f(4) equals to-

If f(x) is an odd pefiodc function defined on the interval [T/2,T/2], where T is rthe perod of f(x). Then phi(x)=int_(a)^(x) f(t)dt, is

Is the function f(x) =sqrt(sinx) periodic?

Let f(x) = sin a x+ cos bx be a periodic function, then

The function f(x)=x-[x] is a periodic with period.

OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Exercise
  1. If h(a)=h(b), the value of the integral inta^b [f(g(h(x))]^(-1)f'(g...

    Text Solution

    |

  2. Given that, F(x)=(1)/(x^(2))int(4)^(x)(4t^(2)-2F'(t))dt, find F'(4).

    Text Solution

    |

  3. It is known that f(x) is an odd function in the interval [p/2, p/2] an...

    Text Solution

    |

  4. Suppose for every integer n, . underset(n)overset(n+1)intf(x)dx = n^(2...

    Text Solution

    |

  5. int(-pi+4)^(pi//4) (tan^(2)x)/(1+a^(x))dx is equal to

    Text Solution

    |

  6. The value of int(0)^(pi//2) cosec(x-pi//3)cosec(x-pi//6)dx is

    Text Solution

    |

  7. The value of int(-1)^(1)(x|x|)dx is equal to

    Text Solution

    |

  8. int0^3 |x^(3)+x^(2)+3x|dx is equal to

    Text Solution

    |

  9. Evaluate: int(-1)^1(x^3+|x|+1)/(x^2+2|x|+1)dx

    Text Solution

    |

  10. Evaluate: int(-pi/2)^(pi/2)log{(a x^2+b x+c)/(a x^2-b x+c)(a+b)|sinx|}...

    Text Solution

    |

  11. For any natural number n, the value of the integral int(0)^(sqrt(n))...

    Text Solution

    |

  12. For any n in R^(+), the value of the integral int(0)^(n[x]) (x-[x])d...

    Text Solution

    |

  13. Let d/(dx)F(x)=((e^(sinx))/x),x > 0. If int1^4 3/x e^sin (x^3)dx=F(...

    Text Solution

    |

  14. The equation int(-pi//4)^(pi//4) {a|sin x|+(b sin x)/(1+cos x)+c}dx=...

    Text Solution

    |

  15. Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in...

    Text Solution

    |

  16. The value of int(alpha)^(beta) x|x|dx, where a lt 0 lt beta, is

    Text Solution

    |

  17. int(-pi//2)^(pi//2) (|x|)/(8 cos^(2)2x+1)dxhas the value

    Text Solution

    |

  18. If [.] denotes the greatest integer function and f(x)={:{(3(x)-(5|x|...

    Text Solution

    |

  19. Find the value of int(-1)^(1)[x^(2)+{x}]dx, where [.] and {.} denote t...

    Text Solution

    |

  20. The value of int(-1)^(1)sin^(-1)[x^(2)+(1)/(2)]dx+int(-1)^(1) cos^(-...

    Text Solution

    |