A) \[\int_{a}^{b}{f\left( \frac{x}{c} \right)}\,dx\]
B) \[\frac{1}{c}\int_{a}^{b}{f(x)\,dx}\]
C) \[\int_{a}^{b}{f(x)\,dx}\]
D) None of these
Correct Answer: C
Solution :
\[I=\frac{1}{c}\int_{ac}^{bc}{f(x/c)dx}\] Put \[\frac{x}{c}=t\Rightarrow dx=c\,dt\] and \[x=bc\Rightarrow t=b\] \[x=ac\Rightarrow t=a\] then, \[I=\int_{a}^{b}{f(t)dt=\int_{a}^{b}{f(x)dx}}\].
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