Integral Calculus Question 351
Question: If $ \int{xe^{2x}dx} $ is equal to $ e^{2x}f(x)+C $ where C is constant of integration, then f(x) is
[UPSEAT 2001]
Options:
A) $ (3x-1)/4 $
B) $ (2x+1)/2 $
C) $ (2x-1)/4 $
D) $ (x-4)/6 $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \int{xe^{2x}dx=\frac{xe^{2x}}{2}}-\int{1.,\frac{e^{2x}}{2}dx} $ $ =\frac{xe^{2x}}{2}-\frac{e^{2x}}{4}+c $ $ =e^{2x}( \frac{2x-1}{4} )+c $
Þ $ f(x)=\frac{(2x-1)}{4}. $
BETA
