Integral Calculus Question 489
Question: If an ant derivative of $ f(x) $ is $ e^{x} $ and that of $ g(x) $ is $ \cos x, $ then $ \int{f(x)\cos x,dx}+\int{g(x)e^{x}dx=} $
[Kerala (Engg.) 2005]
Options:
A) f(x)g(x)+c
B) f(x)+g(x)+c
C) $ e^{x}\cos x+c $
D) f(x) ? g(x)+c
E) $ e^{x}\cos x+f(x)g(x)+c $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \int{f(x)\cos xdx+\int{g(x)e^{x}dx}} $ $ =\int{e^{x}\cos xdx+\int{(-\sin x)e^{x}dx}} $ $ =\frac{e^{x}}{2}(\cos x+\sin x)-\frac{e^{x}}{2}(\sin x-\cos x)+c $ $ =\frac{e^{x}}{2}(2\cos x)+c $ $ =e^{x}\cos x+c $ .
BETA
