MA241-012, Fall 2008Test 2 review sheetDisclaimer: “This review sheet is only intended to give you some guidance, and thus should not be taken asan exhaustive listing of possible test question topics. Do not expect this every time.”Calculators which are not capable of symbolic manipulation are allowed on this test (i.e., no TI-89s, TI-92s,or e quivalent). No other notes or aids will be allowed on this test. For those of you with a TI-89/92, you’llneed to borrow another calculator.The test will cover §§6.2, 6.4, 6.5, 7.1-7.3 (only the first part of §7.3 will be on this test).Note: Unless you are explicitly told not to, you will be expected to fully evaluate all definite integralsthat arise in the course of working a problem.§6.2You need to be able to set up (and, if asked, evaluate) the integral for the volume of solids of revolution.You will have to decide which method to use based on the problem(s) given. Even if not explicitly asked to,you should sketch the region being rotated and the resulting solid to get an idea of which method will workthe best. If you need to find an intersection point for two functions, you may use your calculator to makean educated guess of where it is, but you need to plug your guess back into the functions to verify that itis correct (e.g., it may be clear from a graph that y = x and y = x2intersect at x = 0 and x = 1, but youshould still plug those values into the functions to verify that they’re equal).§6.4You need to know the formula for the average value of a continuous function over an interval. You also needto be able to apply the Mean Value Theorem for Integrals to find c such that f (c) = fav e.§6.5You need to be able to set up (and, if asked, evaluate) the integrals to find the following: the work requiredto lift an object, work required to pump liquid out a tank, and the hydrostatic force on a vertical submergedplate. You may also be asked to explain where each part of your integral is coming from. Eve n if notexplicitly asked to do so, it is helpful to draw a picture of the situation, sketch in a coordinate system, andindicate where everything is with respect to that coordinate system.Moments and centers of mass will not on this test or on the final. As I said in class, the only timeyou will be asked anything related to these types of problems will be in the homework and on the quiz on10/1.1§7.1You need to be able to verify that a function is a solution to a DE (remember that any initial or boundaryconditions need to be satisfied as well). You may be asked to find the constant solutions for a DE.§7.2You need to know the equations for the recursion in Euler’s Method and be able to use Euler’s Method toapproximate the value of the solution to a DE at a given point. Also, given the direction field for some DEand an initial condition, you should be able to sketch the corresponding solution.§7.3You should be able to recognize and solve a separable DE and also apply any given initial or boundaryconditions to find C. Unless the problem states otherwise, you will need to find an explicit solution (i.e.,solve for y). The applications from this section will be on the next