Question

∫e (cos x – sin x) dx is equal to ______ 

(a) e^x sin x + c 

(b) e^x cos x + c 

(c) -e^x cos x + c 

(d) -e^x sin x + c

Answer 1

(b) e^x cos x + c

Let f(x) = cos x 

f'(x) = -sin x 

∫e^x [f(x) + f'(x)] dx = e^x f(x) + c