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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)/(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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