Exam 3 Review MAC 2312 Disclaimer: This review is by no means complete. Please study the homework as well as the lecture notes. These questions should be attempted only after you have completed all the homework assignments. You may need a calculator to solve a couple of these problems, however the exam questions will be choosen in such a way that you do not need a calculator. 1. Section 8.1 Know how to ﬁnd arclength for functions. (a) Find the length of the curve x = y 4 8 + 1 4 y 2 for 1 ≤ y ≤ 2. (Ans: 33 / 16) 2. Section 8.2 Area of a Surface of Revolution. Know the diﬀerence between the rotation about the x-axis and the y-axis!! (a) Find the surface area of y = 1-x 2 for 0 ≤ x ≤ 1 rotated about the y-axis. (Ans: ( π/ 6)(5 √ 5-1)) (b) Find the surface area of x = 1 + y 2 for 1 ≤ y ≤ 2 rotated about the x-axis. (Ans: ( π/ 6)(17 √ 17-5 √ 5)) 3. Section 10.1 Curves of Parametric Equations. Know standard curves, like the circle. (a) Plot
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