Question

You have not proved to me that the Integral of lnsinx w.r.t.x from 0 to pi/2 is equal to:Integral of lnsinx w.r.t.x from 0 to pi/4 plus Integral of lncosx w.r.t.x from 0 to pi/4.

Answer 1

graph sin x from 0 to pi/2

on the same graph plot cos x from 0 to pi/4

Note that cos x from pi/4 to pi/2 is identical to sin x from pi/4 to pi/2 with only a reflection.

Answer 2

Thus for every value of ln sin x from pi/4 to p/2 there is an equal value of ln cos x from 0 to pi/4. Therefore the areas under will be identical.

Answer 3

Damon: That is a good answer which now I really understand.I thank you very much.