Q: ʃʃ cos (x +2y) dy dx where 0 < x < pi; 0 < y < pi/2
When I integrate cos(x+2y) wrt y, do I get sin(x+2y)/2? How do I evaluate sin(x + pi)?
Does sin (x+c) = sin(x) + sin(c)?
The last math course I took was 6 years ago...and then I went straight to multi-variate calc without any review.
Anyway, the formula you gave is if A and B are both variables right? What about in the case that one is a variable and the other is a contant? Do I just treat the constant as a variable and plug it through?
$\displaystyle \int_0^{\pi} \int_0^{\frac{\pi}{2}}\cos (x+2y)~dy~dx $
Ignore the outer integral and do the inner one first.
$\displaystyle \int_0^{\frac{\pi}{2}}\cos (x+2y)~dy$
You can treat x as a constant here. Let $\displaystyle u=x+2y$. Don't forget to change the integration limits. Then you can plug this in the outer integral and the rest is easy..
Also you can use the trigonometric addition formula and Fubini's theorem.