Represents - Calculus - Solved Exam, Exams of Calculus

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Math 106 A Exam 01 page 1 02/01/2013 Name 1. Consider the region S in the plane of all points which are be- tween the graphs of the parabola y = 9 — x? and the straight line y =a +3. The region S is shown in the figure to the right. 1A. Set up the integral which represents the area of S if the corre- sponding approximations are rectangles each of whose base width is Az and each rectangle goes from a top curve down to a bottom curve. That is, the integral is of the form f dr. 1B. Evalate the integral in (1A) to find that area. Show all your work. bee Can opi hf a Me: whieh: 1 = -x) ) ax ‘ ha (2-2) -fiee%-%) (2.33) -(-8.5) 20, $33 “el, fet) | 33s Rey .6- F243 Yt-lot2?_ fe. = 19 ~A+h = 1en ra OS mas 2A. Set up the integral which gives the arc length of the curved part of the boundary of S, that is, the arc length of the graph of y = 9 — 2? from 2 = -3 tor =2. (7 AP de thane £0929 become SOIR de = 2B. The integral in 2A is “doable” — the back of your book has a formula for the antiderivative you'd need. But it’s so complicated, and in practice, a good numerical approximation will do. Indeed, find the MID(50) approximation for the me) il