Unformatted text preview: function on the interval fn/4, n/4'1. L'et A denote the area between the curve whose expression in polar coordinates is r = f(o) (n/4 < o < n/4) andthe two lines o = n/4 and 0 = n/4. Let B denote the area between the curve whose expression in polar coordinates is r=f(0/2) (n/2<o<n/2) andtheverticalaxis a=!n/2. showthat B=zA. You may assume area formulas given in Stewart. (b) (14 points) Find the area between the yaxis and the curve whose expression in polar coordinates is r = sec O/2. You may use the result of part (a) whether or not you have proved it; or you may use any other method that gives the correct answer. 3. (12 points) Find equations in Canesian (i.e., (x,y, z)) and spherical coordinates for the surface described in cylindrical coordinates by the equation y2 = 72 + r. {D [i<tz x 1t2i in IR')....
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 Spring '08
 ISBER
 Trigraph, Coordinate system, Polar coordinate system, Cylindrical coordinate system, Stewart. showthat B=zA

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