To the point:

I was working through past paper questions when I came to this question.

7c

The curve C has the equation:

y=e^{-x}sin x x≥0

The terms of the sequence A_{1}, A_{2}, ..., A_{n},... represent areas between C and the x-axis for successive portions of C where y is positive.

Find an expression for A_{n}in terms of n and π.

Part b of the question asked you to show that the integral of the function was: -1/2 e

^{-x}(sin x + cos x) + c. (by using integration by parts twice and rearranging. )

I managed to derive the result: A

_{n}= 1/2 (e

^{-(2n-1)π/4}+ e

^{-nπ/2})

My question is: is this the result they are asking for, or is there some way to get rid of the exponents?

(Eulers formular: e

^{iπ}=-1 is not on the syllabus)

Any help or advise on this question or anything else to do with this exam would be much appreciated.

Thanks,

Frimble