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)I`

B

I

C

3I

D

6I

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|103 Videos
  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise Level - 1|190 Videos
  • FUNCTIONS

    VMC MODULES ENGLISH|Exercise JEE Main & Advanced|8 Videos
  • INTEGRAL CALCULUS-1

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|25 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)dot If I=int_0^Tf(x)dx , then the value of int_3^(3+3T)f(2x)dx is (a) 3/2I (b) 2I (c) 3I (d) 6I

A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

A continuous real function f satisfies f(2x)=3(f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

A continuous real function f satisfies f(2x)=3(f(x)) AA x in R . If int_0^1 f(x)dx=1, then find the value of int_1^2f(x)dx .

f(x)=int_0^x f(t) dt=x+int_x^1 tf(t)dt, then the value of f(1) is

If f(x)=int_0^x tf(t)dt+2, then

If f is continuous on [0,1] such that f(x)+f(x+1/2)=1 and int_0^1f(x)dx=k , then value of 2k is 0 (2) 1 (3) 2 (4) 3

If f(0)=1,f(2)=3,f'(2)=5 ,then find the value of I_(1)=int_(0)^(1)xf''(2x)dx

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

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Main (Archive)
  1. T h ev a l u eofint0^(pi/2)(dx)/(1+tan^3x)i s 0 (b) 1 (c) pi/2 (d...

    Text Solution

    |

  2. Evaluate the following integral: int0^(pi//2)(sqrt(cotx))/(sqrt(cotx\ ...

    Text Solution

    |

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

    Text Solution

    |

  4. The intercepts on x- axis made by tangents to the curve, y=int(0)^(x)|...

    Text Solution

    |

  5. Ifint(sinx)^1t^2f(t)dt=1-sinx ,w h e r e .x in (0,pi/2), then find th...

    Text Solution

    |

  6. If f(x) is differentiable and int0^(t^2) x f(x) dx=2/5t^5, then f(4/(2...

    Text Solution

    |

  7. If f(x)=int(x^2)^(x^2+1)e^(-t^2)dt , then f(x) increases in

    Text Solution

    |

  8. If I(m,n)=int0^1 t^m(1+t)^n.dt, then the expression for I(m,n) in term...

    Text Solution

    |

  9. Let f(x)=int(1)^(x) sqrt(2-t^(2)) dt, then the real roots of the equa...

    Text Solution

    |

  10. Let f: (0, infty) rarr R and F (x) = int(0) ^(x) f(t) dt . If F(x^(2)...

    Text Solution

    |

  11. The area of the quadrilateral formed by the tangents at the endpoint o...

    Text Solution

    |

  12. The area bounded by the curves y = |x| - 1 and y = -|x| +1 is equal to

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

  14. int(-1)^(1)(x^2+1)dx is equal to

    Text Solution

    |

  15. The area (in sq. units) of the region described by {x,y):y^(2)le2x and...

    Text Solution

    |

  16. The area of the region described by A={(x,y):x^(2)+y^(2)le1 and y^(2)l...

    Text Solution

    |

  17. The area (in square units) bounded by the curves y=sqrt(x),2y-x+3=0, x...

    Text Solution

    |

  18. The area bounded by the curves y=(x-1)^(2),y=(x+1)^(2) " and " y=(1)/(...

    Text Solution

    |

  19. If the area enclosed between the curves y=a x^2a n dx=a y^2(a >0) is 1...

    Text Solution

    |

  20. If the area bounded by the curve y=f(x), x-axis and the ordinates x=1 ...

    Text Solution

    |