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Math 166 Exam 1-Review Supplemental Instruction Iowa State University Leader: Course: Instructors: Date: Max and Jesse Math 166 Dr. Lee and Dr. Martin 9/15/15 1) Find the volume of the solid obtained by rotating the region bounded between y = 𝑥 2 and x = 𝑦 2 about the y-axis by using: a. Shell Method b. Washer Method c. Rotate the same figure around the line x = -1. State the method that you use. 1060 Hixson-Lied Student Success Center 515-294-6624 sistaff@iastate.edu http://www.si.iastate.edu 2) Find the Arc Length of the curve y = (3/4)x4/3 – (3/8)x2/3 +5, 1 ≤ x ≤ 8 3) Set up the integral you would use to find the surface area of the surface obtained 1 by rotating the curve 𝑦 = 𝑒 3𝑥 ( 0 ≤ 𝑥 ≤ 2 ) about the x-axis. Do not evaluate the integral. 4) A spring that obeys Hooke’s Law (F = kx) has a natural length of 10 cm. If a 25 N force is required to keep it stretched to a length of 20 cm, how much work is required to stretch it from 10 cm to 15 cm? 5) Find the work done in pumping water to a height 5 ft. above the top of a conical tank with a height of 20 ft. and a radius of 10 ft. (The cone is inverted, tank is full) Use 𝛿 = 62.4. 6) Find the work done to pump water over the rim of a tank that is 40 feet long and has semicircular ends of radius 8ft. The tank is half full of water. Use 𝛿 = 62.4. 7) Find the centroid of the region bounded by the curves: 𝑦 = 𝑥 2 𝑎𝑛𝑑 𝑦 = 𝑥 + 2