MAC 2313 Midterm: MAC2313 S12 Test 3
Document Summary
Instructions: write your complete solutions on your answer sheets. You are not required to simplify your answers. (1) (20 pts. ) +y2 ex2 dy dx (a) convert the integral to polar coordinates. (b) evaluate the integral. (2) (20 pts. ) Let r be the region in the rst quadrant of the xy-plane lying inside the circle x2 +y2 = 81 and above the line y = x. Let e be the tetrahedron enclosed by the planes x = 0, y = 0, z = 0, and x + y + z = 2. Let e be the solid region inside the cylinder x2 + y2 = 9 and between the two planes z = 0, z = 9 x y. Let r be the region in the rst quadrant of the xy-plane lying between the concentric circles x2 + y2 = 2, x2 + y2 = 4, and between the lines y = 0, y = x.
