Problem

Find the following integrals.

(a) (5 pts) $\displaystyle \int_0^\pi \sin(x)\,dx$.

(b) (5 pts) $\displaystyle \int_0^1 (2x+3)^{1/2}\,dx$.

(c) (5 pts) $\displaystyle \int_0^1 x\ln(x)\,dx$.

(d) (5 pts) $\displaystyle \int_D (2x+3y)\,d(x,y)$, where $D=\{(x,y):|x|+|y|<1\}$.