Question

∫∫sin(x+ y) dA where R = {(x,y)|0<=x < pi, 0<= y <=pi/2} calculate the double integral.

Answer 1

is it use compound angle relation?

Answer 2

you can use that, although it is not necessary.

Answer 3

then what is the alternative way?

Answer 4

how to sketch the region?

Answer 5

\[\large \int\limits_{0}^{\pi} \int\limits_{0}^{\pi/2}\sin(x+y)dy dx=\int\limits_{0}^{\pi}-\cos (x+y)|\begin{matrix}\pi/2 \\ 0\end{matrix}dy\]\[\large \int\limits_{0}^{\pi}(-\cos(\pi/2+x)+\cos (x)) dx\]\[-\sin (\pi/2 + x) + \sin x \huge{| \small \begin{matrix}\pi \\ 0\end{matrix}}\]

Answer 6

ok

Answer 7

let me work out..

Answer 8

is the ans 2

Answer 9

i have the same result.