Home
Class 12
MATHS
If f(t) is a continuous function defined...

If f(t) is a continuous function defined on [a,b] such that f(t) is an odd function, then the function `phi(x)=int_(a)^(x) f(t)dt`

A

is an odd function

B

is an even function

C

is an increasing function on [a,b]

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Chapter Test 1|60 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Chapter Test 2|60 Videos

  • DEFINITE INTEGRALS

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

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA|Exercise Exercise|86 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

If f(t) is an odd function,then varphi(x)=int_(a)^(x)f(t)dt is an even function.

For the function f(x)=int_(0)^(x)(sin t)/(t)dt where x>0

Let f be a continuous function on [a,b]. Prove that there exists a number x in[a,b] such that int_(a)^(x)f(t)dx=int_(x)^(b)f(t)dt

Let f be a continous function on [a,b] . Prove that there exists a number x in [a, b] such that int _(a) ^(x) f(t) dt = int_(x) ^(b) f(t) dt .

In(-4,4) the function f(x)=int_(-10)^(x)(t^(4)-4)e^(-4t)dt has

If f(x) is a continuous function such that f(x) gt 0 for all x gt 0 and (f(x))^(2020)=1+int_(0)^(x) f(t) dt , then the value of {f(2020)}^(2019) is equal to

OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. The value of int(0)^(2pi) cos^(99)x dx, is

    Text Solution

    |

  2. If f(a+x)=f(x), then int(0)^(na) f(x)dx is equal to (n in N)

    Text Solution

    |

  3. If f(t) is a continuous function defined on [a,b] such that f(t) is an...

    Text Solution

    |

  4. If f(x) is an integrable function over every interval on the real line...

    Text Solution

    |

  5. If I(1)=int(3pi)^(0) f(cos^(2)x)dx and I(2)=int(pi)^(0) f(cos^(2)x) th...

    Text Solution

    |

  6. If f(x) is a quadratic polynomial in x such that 6int0^1 f(x)dx-{f(0...

    Text Solution

    |

  7. The value of integral int(-2)^(4) x[x]dx is

    Text Solution

    |

  8. If h(a)=h(b), the value of the integral inta^b [f(g(h(x))]^(-1)f'(g...

    Text Solution

    |

  9. If F(x)=(1)/(x^(2))int(4)^(x) [4t^(2)-2F'(t)]dt then F'(4) equals

    Text Solution

    |

  10. If f(x) is an odd function defined on [-T//2,T//2] and has period T, t...

    Text Solution

    |

  11. If for every integer n, int(n)^(n+1) f(x)dx=n^(2), then the value of ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. The value of int(-1)^(1) x|x|dx, is

    Text Solution

    |

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

    Text Solution

    |

  16. The value of the integral int(0)^(3) (dx)/(sqrt(x+1)+sqrt(5x+1)) is

    Text Solution

    |

  17. int(1)^(-1) (x^(3)+|x|+1)/(x^(2)+2|x|+1)dxis equal to

    Text Solution

    |

  18. int(-pi/2)^(pi//2) log(e ){((ax^(2)+bx+c)/(ax^(2)-bx+c))(a+b)|sinx|}dx...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |