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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`
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