Student number Name [SURNAME(S), Givenname(s)] MATH 101, Section 212 (CSP) Week 3: Marked Homework Assignment Due: Thu 2011 Jan 27 14:00 HOMEWORK SUBMITTED LATE WILL NOT BE MARKED 1. Find the area of the finite plane region bounded by y = 21 x and y 2 = 8 − x, using (a) x as the variable of integration. (b) y as the variable of integration. 2. Find the area of the finite plane region between the curves y = x + 2 and y = x2 , for 0 ≤ x ≤ 3. 3. Find the volume of the solid obtained by rotating the region in the first quadrant where 10 3 ≤ x ≤ 4 and 0 ≤ y ≤ √25−x 2 , about the x-axis. 4. Find the volume of the solid obtained by rotating the finite plane region bounded by the curves x − y 2 = 1 and x − 2y = 1, about the line x = 1. 5. Find the volume of the solid obtained by rotating the region bounded by the curves y = e−x , x = 2 and y = 1, about the line y = 2. 6. Consider a solid whose base is the finite portion of the xy-plane bounded by the curves y = x2 and y = 8 − x2 . The cross sections perpendicular to the x-axis are squares with one side in the xy-plane. Compute the volume of this solid. 7. The base of a solid is the triangular region in the xy-plane with vertices (0, 0), (0, 1) and (1, 0). Cross-sections perpendicular to the base and perpendicular to the y-axis are equilateral triangles. Determine the volume of the solid.