To the point:
I was working through past paper questions when I came to this question.
The curve C has the equation:
y=e-x sin x x≥0
The terms of the sequence A1, A2, ..., An,... represent areas between C and the x-axis for successive portions of C where y is positive.
Find an expression for An 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: An = 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: eiπ=-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.