# Math 172 : Final

Date: Thursday, May 7, 10-11:50am

 Summary Points: The exam will cover Chapter 11 and Methods of integration. There will be no series/sequence problems (ch 10) There will be no application problems (ch 6, 7.7,8.1,8.2) There will be no improper integrals. About 60% will be on Chapter 11 material (11.1-11.4). No review sheets will be posted for Ch 11 but the questions will be similar to homework problems. You should be able to: Compute arclength in parametric and polar coordinates Compute areas in polar coordinates. Compute speed and slopes for parametrically described curves Convert between cartesian, polar and parametric curves. There are several HW problems of this nature and a sample is here. The first 40% will be straight up integral problems (4 integral questions): substitution integration by parts simple trigonometric integrals inverse trig. substitutions simple partial fraction expansions The problems will be similar to those on the review sheet. The  formula sheet  below will be attached to the exam and contains trig. identities needed for certain kinds of integrals. A few additional points Much of the Chapter 11 material also requires integration. Related arclength and area problems, in particular, require integration using algebra tricks (complete the square, factoring, trig identities), inverse trig substitution and trigonometric integrals. It is important you solidly review such methods.  The exam may seem a little trig-heavy in part because of polar coordinates and related polar integrals. You should quickly review both the derivatives and integrals of sin(x), cos(x), tan(x), sec(x). Integrals of the latter two will be on the formula sheet. You may be required to plot simple polar curves especially as they pertain to polar integrals. For inverse trig substitution integration you must, when possible, convert your answer back to "x" without using arccos, arcsin, etc. To be clear, look at this example here. You are required to know sine and cosine of 0,Pi/6,Pi/3,Pi/4,Pi/2 You should be able to do the exam in 75min but will have 1hr 50m.

Formula Sheet that will be attached to Final:

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