MATH128 Final: Math 128 F13 Final Exam Solutions.pdf

• School: University of Waterloo
• Department: Mathematics
• Course: MATH128
• Professor: Clinton Loo

Document Summary

Student name (print legibly) (family name) (given name) Marking scheme: fill in your name, id num- ber, section, and sign the paper. Page: answer all questions in the space provided. The last page is for rough work: check that there are 12 sheets, your grade will be in- Uenced by how clearly you express your ideas, and how well you organize your solutions. Numeri- cal answers should be sim- pli ed as far as possible. Page 2 of 12: evaluate the following integrals. [3] (c) (1 + x)dx sec2(x) tan(x)dx x (x + 1)(x + 2) dx. 2. (a) determine if the following integral converges or diverges. In the case that it converges, evaluate the integral. e(cid:90) ln(x)dx. [3] (b) consider the region bounded by x + y = 1, x-axis and y-axis. Suppose this region is rotated about the x-axis. Determine the volume of the solid obtained by revolving the region.