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

`3/2I`

B

`2I`

C

`3I`

D

`6I`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `I_(1)=int_(3)^(3+3T) f(2x)dx`
Put `2x=y` so that `I_(1)=1/2int_(6)^(6+6T)f(y)dy`
`=1/2 6int_(0)^(T)dy` [ `:' f(x)` has period `T`]
`=3I`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise MCQ_TYPE|27 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise LC_TYPE|31 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CAE_TYPE|88 Videos

  • CURVE TRACING

    CENGAGE PUBLICATION|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 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

let T le0 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 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

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

Let f:RtoR be a continuous function which satisfies f(x)=int_(0)^(x)f(t)dt . Then the value of f(log_(e)5) is

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(agt0) and int_(0)^(T)f(x)dx=2 , then find the value of int_(0)^(a)f(x)dx .

If f(x)=x+int_(0)^(1)t(x+t)f(t)dt , then the value of (23)/(3)f(0) is equal to-

if f(x) is a function such that f(x+k)=f(x) for K in I^+ and I=int_0^k f(x)dx then I=int_0^(k^(2-k))f(x)dx is equal to

If int_a^b(f(x)-3x)dx=a^2-b^2 then the value of f(pi/6) is ___

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

CENGAGE PUBLICATION-DEFINITE INTEGRATION -SCQ_TYPE
  1. about to only mathematics

    Text Solution

    |

  2. The value of int(-pi)^( pi)sum(r=0)^(999)cos rx(1+sum(r=1)^(999)sin rx...

    Text Solution

    |

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

    Text Solution

    |

  4. int1^4 {x-0.4}dx equals (where {x} is a fractional part of x

    Text Solution

    |

  5. The value of int0^x[cost]dt ,x in [(4n+1)pi/2,(4n+3)pi/2]a n dn in N ...

    Text Solution

    |

  6. Evaluate: int0^(2pi)[sinx]dx ,w h e r e[dot] denotes the greatest int...

    Text Solution

    |

  7. int0^x(2^t)/(2^([t]))dt ,w h e r e[dot] denotes the greatest integer f...

    Text Solution

    |

  8. Let f be an odd continous function which is periodic with priod 2 if g...

    Text Solution

    |

  9. If g(x)=int0^x(|sint|+|cost|)dt ,then g(x+(pin)/2) is equal to, where...

    Text Solution

    |

  10. Ifx=intc^(sint)sin^(-1)z dz ,y=intk^(sqrt(t))(sinz^2)/zdz ,t h e n(dy)...

    Text Solution

    |

  11. Let f(x)=int2^x(dt)/(sqrt(1+t^4))a n dg(x) be the inverse of f(x) . Th...

    Text Solution

    |

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

    Text Solution

    |

  13. If f(x)=cosx-int0^x(x-t)f(t)dt ,t h e nf^(prime)(x)+f(x) is equal to -...

    Text Solution

    |

  14. A function f is continuous for all x (and not everywhere zero) such th...

    Text Solution

    |

  15. lim(x->0)1/x[inty^a e^(sin^2t)dt-int(x+y)^a e^(sin^2t)dt] is equal to

    Text Solution

    |

  16. Let f(x) =int1^x e^t/tdt,x in R^+ . Then complete set of valuesof x f...

    Text Solution

    |

  17. If int0^xf(t) dt=x+intx^1 tf(t)dt, then the value of f(1)

    Text Solution

    |

  18. If f(x)=1+1/x int1^x f(t) dt, then the value of f(e^-1) is

    Text Solution

    |

  19. If [f((sqrt(3))/2)] is [.] denotes the greatest integer function)

    Text Solution

    |

  20. f(x) is continuous function for all real values of x and satisfies int...

    Text Solution

    |