Home
Class 12
MATHS
Let T >0 be a fixed real number. Suppose...

Let `T >0` be a fixed real number. Suppose `f` is continuous function such that for all `x in R ,f(x+T)=f(x)dot` If `I=int_0^Tf(x)dx ,` then the value of `int_3^(3+3T)f(2x)dx` is `3/2I` (b) `2I` (c) `3I` (d) `6I`

A

`(3)/(2)l`

B

`2l`

C

`3l`

D

`6l`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 6|10 Videos
  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|34 Videos
  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 4|20 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

Let T>0 be a fixed real number.Suppose f is continuous function such that for all x in R,f(x+T)=f(x)* If I=int_(0)^(T)f(x)dx then the value of int_(3)^(3+3T)f(2x)dx is (a) (3)/(2)I( b) 2I( c) 3I(d)6I

Let Tgt0 be a fixed real number. Suppose f is a cintinuous function such that f(x+T) = f(x) "for all" x in R . If I=int_(0)^(T) f(x)dx, then the vlaue of int_(3)^(3+3T) f(2x)dx is

I=int_(0)^(T)f(x)dx, then show that int_(3)^(3+3T)f(2x)dx=3I

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

Let f(x) be a continuous and periodic function such that f(x)=f(x+T) for all xepsilonR,Tgt0 .If int_(-2T)^(a+5T)f(x)dx=19(ag0) and int_(0)^(T)f(x)dx=2 , then find the value of int_(0)^(a)f(x)dx .

Let: f:[0,3]vecR be a continuous function such that int_0^3f(x)dx=3. If I=int_0^3(xf(x)+int_0^xf(t)dt)dx , then value of I is equal to

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise For Session 5
  1. The value of int-1^10 sgn (x -[x])dx is equal to (where, [:] denotes t...

    Text Solution

    |

  2. the value of int(0)^([x]) dx (where , [.] denotes the greatest integer...

    Text Solution

    |

  3. Evaluate: int(-pi/4)^(npi-pi/4)|sinx+cosx|dx

    Text Solution

    |

  4. Let f (x) = x – [x], for every real number x, where [x] is the greates...

    Text Solution

    |

  5. f(x)=int0^xf(t)dt=x+intx^1tf(t)dt ,t h e nt h ev a l u eoff(1)i s 1/2...

    Text Solution

    |

  6. The least value of the function phi(x)=overset(x)underset(5pi//4)int...

    Text Solution

    |

  7. The poins of extremum of phi(x)=underset(1)overset(x)inte^(-t^(2)//2)...

    Text Solution

    |

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

    Text Solution

    |

  9. Let d/(dx) (F(x))= e^(sinx)/x, x>0. If int1^4 2e^sin(x^2)/x dx = F(k)...

    Text Solution

    |

  10. Let f:(0,oo)to R and F(x)=int(0)^(x) f(t)dt. " If " F(x^(2))=x^(2)(1+x...

    Text Solution

    |

  11. Let T >0 be a fixed real number. Suppose f is continuous function such...

    Text Solution

    |

  12. Let f(x)=int1^xsqrt(2-t^2)dtdot Then the real roots of the equation , ...

    Text Solution

    |

  13. Let f(x) be an odd continuous function which is periodic with period...

    Text Solution

    |

  14. Let f(x) be a function defined by f(x)=int1^xt(t^2-3t+2)dt,1<=x<=3 The...

    Text Solution

    |

  15. The value of lim(x rarr0)(2int(0)^(cos x ) cos^(-1) (t))/(2x- sin 2 x)...

    Text Solution

    |

  16. If underset(0)overset(x)int (bt cos 4 t - a sin 4t)/( t^(2))dt=(a sin ...

    Text Solution

    |

  17. If f(x)=int0^x{f(t)}^(- 1)dt and int0^1{f(t)}^(- 1)=sqrt(2), then

    Text Solution

    |

  18. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  19. Concider the function defined on [0,1] rarr R f(x) =(sinx- cosx)/(x^(2...

    Text Solution

    |

  20. Concider the function defined on [0,1] rarr R f(x) =(sinx- cosx)/(x^(2...

    Text Solution

    |