M-172Q Midterm: Montana State MATH 172 Exam1
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16 may 2013: integrate. (a) [5] z ypy + 3 dy. 0 sin ( 2x) dx (c) [6] z. 1 + x6 dx (e) [2] z 3x2 + 6x5. 1 + x6 dx [see above. : [10] sketch the region enclosed by y = 5x x2 and y = x2. 3x and compute its area: [10] show the volume of a sphere of radius r is v = 4. 3 r3 by computing the volume of the solid generated by rotating the semicircle y = r2. Consider the region bounded by the curves y = x2 and y = x. (a) [5] sketch the region. (b) [5] express the volume of the solid obtained by rotating the region about the x-axis using the disk method. Do not integrate. (c) [5] express the volume of the solid obtained by rotating the region about the x-axis using the shell method.
