What is $\int_D x\sin(y)\ dA$ where $D$ is the half circle centered at $(0,0)$ with radius $1$ above the $x$ axis.
So I got $$ \int_0^1 \int_0^\pi r\cos(\theta)\sin(r \sin(\theta))\ r\ dr\ d \theta. $$ Then I don't know how to continue.
2026-03-28 08:09:30.1774685370
calculate the integral of $\int_D x\sin(y)$
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HINT
Substitute $u = \sin \theta$ then $du = \cos \theta d\theta$ and $$ \iint r\cos(\theta)\sin(r \sin(\theta))\ r\ dr\ d \theta = \int r^2 \left[ \int \sin(ru) du \right] dr $$