MATH 221 Midterm: Kansas State MATH 221 221t2s17
7 Mar 2019
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Show all your work in the space provided under each question. Please write neatly and present your answers in an organized way. You may use your one sheet of notes, but no books or calculators. The chart below indicates how many points each problem is worth. /60: express the improper integral as a limit, and evaluate. X: a force of 400 pounds will stretch a spring two feet from its equilibrium or natural length. Find the work (in foot-pounds) required to stretch the spring from two feet to three feet beyond its equilibrium length: find the centroid of the region under y = x3 for. Z sinh2(x) cosh3(x) dx: find the arc length of the curve. y = ln(cos(x)) for 0 x . 4: use the method of cylindrical shells to nd the volume of revolution formed by rotating around the y-axis the region under the curve y = x x2 4 for.
