MAT-2130 Midterm: MATH 2130 App State Spring2016 Test1 answer key
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Name: x = cos( ) sin( ) y = sin( ) sin( ) z = 2 (1 + cos(2 ): (14 points) use a double riemann sum to approximate zz y2e x da where r = [ 4, 2] [ 1, 5]. Use midpoint rule and a 3 2 grid of rectangles (3 across and 2 up) to partition r. (don"t worry about simplifying. : (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. Y px3 + 1 dx dy: (14 points) find the centroid of r = {(x, y)| x2 + y2 9 and x 0} (the right-half of the disk of radius 3 centered at the origin). Feel free to use what you know about areas of circles and symmetry to cut down the number of integrals you need to evaluate. m = zzr.
