Definite Integration Question 357
Question: Assume that $ f $ is continuous everywhere, then $ \frac{1}{c}\int_ac^{bc}{f( \frac{x}{c} )}dx= $
Options:
A) $ \int_a^{b}{f( \frac{x}{c} )}dx $
B) $ \frac{1}{c}\int_a^{b}{f(x)dx} $
C) $ \int_a^{b}{f(x)dx} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ I=\frac{1}{c}\int_ac^{bc}{f(x/c)dx} $
Put $ \frac{x}{c}=t\Rightarrow dx=cdt $ 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}} $ .
BETA
