MAT-2130 Midterm: MATH 2130 App State summer2015 Test3
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Name: answer key: (10 points) use a double riemann sum to approximate zz. R px + y2 da where r = [0, 30] [ 1, 3]. Use midpoint rule and a 3 2 grid of rectangles (3 across and 2 up) to partition r. (don"t worry about simplifying. ) R px + y2 da 10 2(cid:16)p5 + 02 +p15 + 02 +p25 + 02. +p5 + 22 +p15 + 22 +p25 + 22(cid:17: (10 points) let r be the region bounded by y = 3x2 and y = 16 x2. (a) sketch the region r. [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 . However, as an x-simple region, we"ll have to split it into 2 pieces.
