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:
- $\int _3^{3+3 T} f(2 x) d x$ Put $2 x=y \Rightarrow d x=\frac{1}{2} d y$
$$ \therefore \quad \frac{1}{2} \int _6^{6+6 T} f(y) d y=\frac{6 I}{2}=3 I $$
