Let and be non–zero real numbers.

MATHEMATICS · Multi-part · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

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