Question

Integration of (Sin(x) + Cos(x))e^x is______________

(a) e^x Cos(x)

(b) e^x Sin(x)

(c) e^x Tan(x)

(d) e^x (Sin(x)+Cos(x))

The question was asked by my school principal while I was bunking the class.

Origin of the question is Improper Integrals topic in chapter Integral Calculus of Engineering Mathematics

Answer 1

The correct option is (b) e^x Sin(x)

The best explanation: Let f(x) = e^x Sin(x)

∫ e^x Sin(x)dx = e^x Sin(x) – ∫ e^x Cos(x)dx

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