MAT-2130 Midterm: MATH 2130 App State summer2014 Test3
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Be sure to show your work: (10 points) use a double riemann sum to approximate zzr. Use midpoint rule and a 2 3 grid of rectangles (2 across and 3 up) to partition r. x sin(y2) da where r = [1, 9] [ 1, 2]. (don"t worry about simplifying. ) Zzr x sin(y2) da 4 1(cid:20)3 sin (cid:18) 1. 2(cid:19)2! (cid:21: (10 points) let r be the region bounded by y = x 2 and y = 4 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 x da using the order of integration dy dx . Don"t evaluate the integral. (c) set up the integral rrr x da using the order of integration dx dy . Don"t evaluate the integral. (a) setting our bounds equal, x 2 = 4 x2. Z 2 x 2 x dy dx. (c) these bounds are slightly trickier.
