Integral Calculus Question 154
Question: If $ \int{g(x)dx=g(x),} $ then $ \int{g(x){f(x)+f’(x)}dx} $ is equal to
Options:
A) $ g(x)f(x)-g(x)f’(x)+C $
B) $ g(x)f’(x)+C $
C) $ g(x)f(x)+C $
D) $ g(x)f^{2}(x)+C $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \int{g(x){f(x)+f’(x)}dx} $ $ =\int{g(x)f(x)dx+\int{g(x)f’(x)dx}} $ $ =f(x)\int{g(x)dx}-\int{f’(x)g(x)dx+\int{g(x)f’(x)dx}} $ $ =f(x)g(x)-\int{f’(x)g(x)dx+\int{g(x)f’(x)dx}} $ [Given $ \int{g(x)dx=g(x)} $ ] $ =f(x)g(x)+c$
BETA
