MATH 221 Midterm: Kansas State MATH 221 221t2s06
7 Mar 2019
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In each of the following problems, show your work, and organize your work clearly, so as to maximize the opportunities for partial credit . For example, in all but one of the problems, it will be a good idea to make some sort of diagram showing the. Element ds, or ds, or df , etc, (16 pts) 1. Find the area enclosed by the cardioid which, in polar coordinates, is given by the equation r = 1 + sin . (16 pts) 2. Find the length of the curve c parametrized by x = 1. Find the area of the surface obtained by revolving the graph of y = sin x around the x-axis, as x goes from 0 to /2. Find the centroid c(x, y) for the upper half of the circle of radius 4 centered at the origin. Express the equation r = 8 sin + 6 cos in the form (x h) a2 + (y k)2 b2.
