Let Tgt0 be a fixed real number. Suppose...

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

A

`(3)/(2) I`

B

2I

C

3I

D

6I

Text Solution

Verified by Experts

The correct Answer is:

C

We have, `underset(0)overset(T)int f(x)dx,`
Let , `I_(1) = underset(3) overset(3+3T)int f(2x)dx`
`rArr I_(1) =(1)/(2) underset(6) overset(6+6T)int f(t)dx` where t=2x.
`rArr I_(1) =(1)/(2)xx6 underset(0) overset(T)int f(t)dx" " [ :. underset(a)overset(a+nT)int f(x)dx =underset(0)overset(T)int f(x) dx]`
`rArr I_(1)=3I`

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