Home
Class 12
MATHS
Let f:R in R be a continuous function su...

Let `f:R in R` be a continuous function such that f(x) is not identically equal to zero. If `int_(0)^(x) |x-2|dx,x ge 0`. Then, f'(x) is

A

an even function

B

an odd function

C

a periodic function

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Chapter Test 2|60 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Exercise|147 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

Let f(x) =int_(0)^(x) |xx-2|dx, ge 0 . Then, f'(x) is

Let f(x) be a continuous function in R such that f(x) does not vanish for all x in R . If int_1^5 f(x)dx=int_-1^5 f(x)dx , then in R, f(x) is (A) an even function (B) an odd function (C) a periodic function with period 5 (D) none of these

Let f : R to R be continuous function such that f (x) + f (x+1) = 2, for all x in R. If I _(1) int_(0) ^(8) f (x) dx and I _(2) = int _(-1) ^(3) f (x) dx, then the value of I _(2) +2 I _(2) is equal to "________"

Let f:R to R be continuous function such that f(x)=f(2x) for all x in R . If f(t)=3, then the value of int_(-1)^(1) f(f(x))dx , is

A continous function f(x) is such that f(3x)=2f(x), AA x in R . If int_(0)^(1)f(x)dx=1, then int_(1)^(3)f(x)dx is equal to

If f(x) is a continuous function such that f(x)|0,AA x in[2,10] and int_(4)^(8)f(x)dx=0 then find

Let f (x) be a conitnuous function defined on [0,a] such that f(a-x)=f(x)"for all" x in [ 0,a] . If int_(0)^(a//2) f(x) dx=alpha, then int _(0)^(a) f(x) dx is equal to

Let f : [-1, 2]to [0, oo) be a continuous function such that f(x)=f(1-x), AA x in [-1, 2] . If R_(1)=int_(-1)^(2)xf(x)dx and R_(2) are the area of the region bounded by y=f(x), x=-1, x=2 and the X-axis. Then :

OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 1
  1. Let I(n)=int(0)^(pi//2) sin^(n)x dx, nin N. Then

    Text Solution

    |

  2. If f(x)=int(0)^(x) sin^(4)t dt, then f(x+2pi) is equal to

    Text Solution

    |

  3. int(0)^(pi) (1)/(1+3^(cosx)) dx is equal to

    Text Solution

    |

  4. Let int(0)^(a) f(x)dx=lambda and int(0)^(a) f(2a-x)dx=mu. Then, int(...

    Text Solution

    |

  5. The value of int(pi//4)^(3pi//4) (x)/(1+sin x) dx is equal to

    Text Solution

    |

  6. Let I(n)=int(0)^(pi//2) cos^(n)x cos nx dx. Then, I(n):I(n+1) is equal...

    Text Solution

    |

  7. The value of int(-1)^(1) max[2-x,2,1+x] dx is

    Text Solution

    |

  8. int(0)^(pi//4) sin(x-[x]) dx is equalto

    Text Solution

    |

  9. The value of the integral int(-1)^(1) (x-[2x])dx,is

    Text Solution

    |

  10. Let f:R in R be a continuous function such that f(1)=2. If lim(x to 1)...

    Text Solution

    |

  11. Let f:R in R be a continuous function such that f(x) is not identicall...

    Text Solution

    |

  12. Let f(x)=int(0)^(x) |xx-2|dx, ge 0. Then, f'(x) is

    Text Solution

    |

  13. Lt(nrarroo) {(n!)/(kn)^n}^(1/n), k!=0, is equal to (A) k/e (B) e/k (C)...

    Text Solution

    |

  14. Let f(x) be an integrable function defined on [a,b],b gt a gt 0. If I(...

    Text Solution

    |

  15. int(0)^(sqrt(2)) [x^(2)]dx, is

    Text Solution

    |

  16. Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be a...

    Text Solution

    |

  17. (sum(n=1)^10int(-2n-1)^(-2n)sin^(27)(x)dx+sum(n=1)^10int(2n)^(2n+1)sin...

    Text Solution

    |

  18. If f(y)=e^(y)=e^(y),g(y)=y, y gt 0 and F(t)=int(0)^(t) f(t-y)g(y) dy, ...

    Text Solution

    |

  19. If I(n)=int(0)^(pi//2) x^(n) sin x dx, then I(4)+12I(2) is equal to\

    Text Solution

    |

  20. int(0)^(1) sin{2 tan^(-1)sqrt((1+x)/(1-x))}dx=

    Text Solution

    |