http://img207.imageshack.us/img207/9109/math1yk3.png

In the solution, it is amazingly simple, but i don't understand why they do what they did.

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- Oct 28th 2006, 10:22 PMscorpion007help with integral
http://img207.imageshack.us/img207/9109/math1yk3.png

In the solution, it is amazingly simple, but i don't understand why they do what they did. - Oct 28th 2006, 11:01 PMCaptainBlack
It is because of the symmetry of the cosine curve (actually the anti-symmetry

of cos about pi/2) guarantees that the part of the area above y=b/2 fits

exactly (when rotated through 90 degrees) above the part from a/2 to form

a rectangle of length a and width b/2.

RonL - Oct 29th 2006, 07:34 AMSoroban
Hello, scorpion007!

Quote:

http://img207.imageshack.us/img207/9109/math1yk3.png

In the solution, it is amazingly simple, but i don't understand why they do what they did.

We could have tried: .

. . but it is far easier to integrate with respect to

We have: . .

. . .

So we have: .

. .

. . . . . answer (c)

- Oct 29th 2006, 07:52 AMCaptainBlack
- Oct 29th 2006, 03:53 PMscorpion007
ah, thank you, in my original attempt at integration, i made a stupid algebraic mistake, which caused the answer to be wrong. In general, that's is how i attempted it the first time, before reading what CaptainBlack said.