Home
Class 12
MATHS
Let f(x) be an odd continous function wh...

Let f(x) be an odd continous function which is periodic with period 2. If ` g(x)=int_(0)^(x) f(t) dt` , then

A

`g(x)` is odd function

B

`g(2x)=1`

C

`g(2x)=0`

D

`g(x)` is even function

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Linked Comprehension Type Questions|11 Videos
  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Assertion-Reason Type Questions|15 Videos
  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Objective Type Questions (Only one answer)|70 Videos
  • DIFFERENTIAL EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section - J (Aakash Challengers Questions)|4 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT (SECTION - J)(ANKASH CHALLENGERS QUESTIONS)|4 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be an odd continuous function which is periodic with period 2. if g(x)=underset(0)overset(x)intf(t)dt , then

Let f(x) = int_(-2)^(x)|t + 1|dt , then

Let f(x) = int_(0)^(x)|2t-3|dt , then f is

Let f(x) be a continuous function which takes positive values for xge0 and satisfy int_(0)^(x)f(t)dt=x sqrt(f(x)) with f(1)=1/2 . Then

Let a function f be even and integrable everywhere and periodic with period 2. Let g(x)=int_0^x f(t) dt and g(t)=k The value of g(x+2)-g(x) is equal to (A) g(1) (B) 0 (C) g(2) (D) g(3)

Let a function f be even and integrable everywhere and periodic with period 2. Let g(x)=int_0^x f(t) dt and g(t)=k The value of g(2) in terms of k is equal to (A) k (B) 2k (C) 3k (D) 5k

Let f(x)=int_(2)^(x)f(t^(2)-3t+4)dt . Then

Let a function f be even and integrable everywhere and periodic with period 2. Let g(x)=int_0^x f(t) dt and g(t)=k For what value of g in terms of k is

Given an even function f defined and integrable everywhere and periodic with period 2 . Let g(x)=int_0^x f(t) dt and g(t)=k for what values of g in terms of k

Let f(x) and phi(x) are two continuous function on R satisfying phi(x)=int_(a)^(x)f(t)dt, a!=0 and another continuous function g(x) satisfying g(x+alpha)+g(x)=0AA x epsilonR, alpha gt0 , and int_(b)^(2k)g(t)dt is independent of b If f(x) is an odd function, then

AAKASH INSTITUTE ENGLISH-INTEGRALS-Objective Type Questions (More than one answer)
  1. If primitive of sin (log x) is f(x)*{sin g(x)- cos h(x)}+c, (c being c...

    Text Solution

    |

  2. If int cos^(-1)x+cos^(-1)sqrt(1-x^2) dx= Ax+f(x)sin^(-1)x-2sqrt(1-x^2)...

    Text Solution

    |

  3. If int (3x+4)/(x^3-2x-4) \ dx = log|x-2| + k logf(x) + c, then (i) f...

    Text Solution

    |

  4. A primitive of sin 6x is

    Text Solution

    |

  5. If int(sinx)/(sin(x-a))dx=f(x)sina+g(x)cosa+c, then

    Text Solution

    |

  6. If f(x)=int1^x(lnt)/(1+t)dt where x>0, then the values of of x satisfy...

    Text Solution

    |

  7. The value of int0^oo(x dx)/((1+x)(1+x^2)) is equal to

    Text Solution

    |

  8. If f(x)=int0^x(sint)/t dt ,x >0, then

    Text Solution

    |

  9. The value of int0^1(2x^2+3x+3)/((x+1)(x^2+2x+2))dx is

    Text Solution

    |

  10. inta^b sgn(x)dx equals (a,b in R)

    Text Solution

    |

  11. IfAn=int0^(pi/2)(sin(2n-1)x)/(sinx)dx ,bn=int0^(pi/2)((sinn x)/(sinx))...

    Text Solution

    |

  12. int0^1 sin(x^2+2x+1)dx-int1^2 sinx^2 dx is equal to (i)0 (ii)1 (ii...

    Text Solution

    |

  13. Ifx=int0^y(dt)/(sqrt(1+9t^2))a n d(d^2y)/(dx^2)=a y ,t h e nfin da

    Text Solution

    |

  14. The integral underset(0)overset(pi)int x f(sinx )dx is equal to

    Text Solution

    |

  15. Let f(x) be an odd continous function which is periodic with period 2....

    Text Solution

    |

  16. If I=overset(4)underset(3)int (1)/(3sqrt(logx))dxthen

    Text Solution

    |

  17. Let f : (0,oo) to R and F(x)=int(0)^(x)t f(t)dt. If F(x^(2))=x^(4)+x...

    Text Solution

    |

  18. Let l(1)=int(1)^(10^(4))({sqrt(x)})/(sqrt(x))dx and l(2)=int(0)^(10)x{...

    Text Solution

    |

  19. If f(x)=x^(2)int(0)^(1)f(t)dt+2, then

    Text Solution

    |

  20. If f(x)=int0^x tf(t)dt+2, then

    Text Solution

    |