Mathematics MATH S-1a Final: solution to common calculus question exam

• School: Harvard University
• Department: Mathematics
• Course: Mathematics MATH S-1a

Document Summary

Fill in the answer to each problem on your scantron. Make sure your name, section and instructor is on your scantron: find the area of the region enclosed by y = x and y = 5x x2. a) d) 3: set up the integral representing the volume of the solid obtained by rotating the region bounded by y = x2 + 1 and y = 3 x2 about the x-axis, z 1. [(3 x2)2 (x2 + 1)2] dx. 2 x [(3 x2) (x2 + 1)] dx: z 1. [(x2 + 1)2 (3 x2)2] dx. 2 x [(x2 + 1) (3 x2)] dx. [(x2 + 1)2 (3 x2)2] dx: none of the above, evaluate z. 1 + x2 dx is convergent or divergent. 2 , convergent: set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve y = e2x, 0 x 1 about the x-axis, z 1.