Question 7
In each of the following, sketch the region D, and hence evaluate their integrals corresponding to the
region D.
(a) \iint_D \frac{xy}{x^2+1} dA, D = \{(x, y) | 0 \le x \le 1, 0 \le y \le \sqrt{x}\}
(b) \iint_D x^3 y^2 dA, D = \{(x, y) | 0 < x < 3 - y < 2\}
(c) \iint_D x \cos y dA, where D is a region on the xy-plane bounded by $y = 0$, $y = x^2$ and $x = 1$.
(d) \iint_D y^2 e^y dA, where D is a region on the xy-plane bounded by $y = x$, $y = 4$, and $x = 0$.
(e) \iint_D y^3 dA, where D is a triangular region on the xy-plane with vertices $(0, 2)$, $(1, 1)$, and
$(3, 2)$.
