Mathematics

Problem

Let

a

and

b

be non–zero real numbers. a. Derive a closed–form expression for

I = \displaystyle \int e^{ax}\sin bx\,dx

in terms of

a

b

x

and elementary functions, including the constant of integration. b. Hence obtain a corresponding formula for

K = \displaystyle \int e^{ax}\cos bx\,dx

." c. State the simplified forms of your answers to parts (i) and (ii) when

a=0