MAT-2130 Midterm: MATH 2130 App State Spring2013 Test1 answer key
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Be sure to show your work! x = cos( ) sin( ) y = sin( ) sin( ) z = Sketch the region of integration and then evaluate the integral. Hint: r sin(y3) dy is impossible to evaluate. sin(y3) dy dx. /14 points) consider the integral zz (2x + y) cos(3x y) da where r is bounded by y = 2x, y = 2x + 1, y = 3x 2, and y = 3x 3. State a change of coordinates: u =??? and v =??? so that the resulting integral can be evaluated. Perform the change of coordinates, but do not evaluate the integral. /15 points) consider the integral: i = z 4. 4z 0 (a) rewrite i in the following order of integration: rrr. 16 x2 z 0 dx dz dy. (b) rewrite i in terms of cylindrical coordinates. Do not evaluate the integral. (c) rewrite i in terms of spherical coordinates.
