MAT-2130 Midterm: MATH 2130 App State Spring2013 Test3
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Be sure to show your work: (14 points) use a double riemann sum to approximate zzr. Use midpoint rule and a 3 2 grid of rectangles (3 across and 2 up) to partition r. y2e x da where r = [ 4, 2] [ 1, 5]. (don"t worry about simplifying. ) We have 4 x 2 is to be partitioned into 3 pieces so that x = 1 y 5 is to be partitioned into 2 pieces so that y = the left sums up the partition information. 2(cid:19)2 e3 +(cid:18) 1 y2e x da 2 3 "(cid:18) 1. 0 z 2: (14 points) first, sketch the region of integration and then evaluate z 4. Hint: r x3 + 1 dx cannot be expressed in terms of elementary functions that is you can"t integrate it. The bounds tell us that the region of integration is de ned by 0 y 4 and y x 2.
