Math 280 Practice Problems for Exam 3
15.2 - Double Integrals over General Regions
1. Evaluate the double integral
(a) \iint_R (x^2 + 2y)dA, R is bounded by $y = x$, $y = x^2$, $x \ge 0$
(b) \iint_R 2xydA, R is the triangular region with vertices (0, 0), (1, 2), and (0, 3).
2. Find the volume of the solid bounded by the cylinder $y^2 + z^2 = 4$ and the plane $x = 2y$, $x = 0$, $z = 0$ in the
first octant.