Indefinite Integration 2 Question 2

2. Let $T>0$ be a fixed real number. Suppose, $f$ is a continuous function such that for all $x \in R . f(x+T)=f(x)$. If $I=\int _0^{T} f(x) d x$, then the value of $\int _3^{3+3 T} f(2 x) d x$ is

$(2002,1 M)$

(a) $\frac{3}{2} I$

(b) $I$

(c) $3 I$

(d) $6 I$

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Answer:

Correct Answer: 2. (c)

Solution:

  1. $\int _3^{3+3 T} f(2 x) d x$ Put $2 x=y \Rightarrow d x=\frac{1}{2} d y$

$$ \therefore \quad \frac{1}{2} \int _6^{6+6 T} f(y) d y=\frac{6 I}{2}=3 I $$



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