MAT-2130 Midterm: MATH 2130 App State summer2016 Test1 answer key
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Name: x = cos( ) sin( ) y = sin( ) sin( ) z = 2 (1 + cos(2 ): (10 points) use a double riemann sum to approximate zz. R px + y2 da where r = [0, 30] [ 1, 3]. [warning: one of the integrals below will have to be split into 2 pieces. ] (b) set up the integral rrr yex da using the order of integration dy dx . Don"t evaluate the integral. (c) set up the integral rrr yex da using the order of integration dx dy . Don"t evaluate the integral: (10 points) compute z 2. Hint: you cannot integrate r cos(x2) dx in terms of elementary functions: (12 points) let e be the region bounded by z = 0 and z = 4 x2 y2 and such that y 0. A graph of this region is ever so kindly provided to the right.
