Integral Calculus Question 406
If $ \int{f(x),dx}=F(x)+C}, $ then $ {{\int{
[ f(x) ]}}^{2}}dx $ is [DCE 2002]
Options:
A) $ \frac{1}{2}{{[ f( x ) ]}^{2}} $
B) $ {{[ f( x ) ]}^{3}} $
C) $ \frac{{{[ f( x ) ]}^{3}}}{3} $
D) $ {{[ ,f( x ) ]}^{2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
Trick : Let $ f(x)=e^{x}, $ then $ \int{f(x)dx}=f(x)+C $ $ \therefore ,\int{{{(e^{x})}^{2}}dx=\frac{e^{2x}}{2}+C=\frac{1}{2}{{[f(x)]}^{2}}.} $
BETA
