Question

Integration of (Sin(x) – Cos(x))e^x is ___________

(a) -e^x Cos(x)

(b) e^x Cos(x)

(c) -e^x Sin(x)

(d) e^x Sin(x)

I got this question during an online exam.

This interesting question is from Improper Integrals topic in chapter Integral Calculus of Engineering Mathematics

Answer 1

The correct choice is (a) -e^x Cos(x)

The best I can explain: Add constant automatically

Let f(x) = e^x Sin(x)

∫ e^x Sin(x)dx = -e^x Cos(x) + ∫ e^x Cos(x)dx

∫ e^x Sin(x)d-∫ e^x Cos(x)dx = ∫ e^x [Sin(x)-Cos(x)]dx = -e^x Cos(x).