# B 3 pts the volume of the solid obtained by rotating

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(b) (3 pts) The volume of the solid obtained by rotating tlie region bounded by y = ex, y x = 0, and x = = aa.bout tlie y-axis. = x3,
2. Express the following quantities in terms of the definite integral. Show your work clearly. DO NOT EVALUATE THE INTEGRALS. (a) (2 pts) The volume whose height is h and whose cross-section at height z is a rectangle with dimensions z and h (b) (4 pts) A solid with a circular base of radius L. and whose sections perpendicular to a particular diameter of the base are equilateral triangles. - z. 'i\r bm, bj 5 . b ~ ;D gjan by -h.e re &P bounded bg J x2+ lz =q 5 i n a Akb a e ir 5 m ~ e t r i i abut 3ikcA- u x i s we i) - - 1 Can i h t e r d e bnlX - a -b i= 2 and & 3 'b I dX Given a r r o s 5erh.m A+ x = a , O S O , I Z wc
Please printnames and IDs in ink: NSID: Family Name: KEY| First Name: | Student ID: INSTRUCTIONS 5. Write clearly and legibly.1. Time Limit: 30 minutes6. Simplify all answers unless otherwise instructed.2. Closed book. Closed notes. 7. Show your work; insufficient work shown may not be credited. 3. No copying. No calculators. MATH 124 CALCULUS II for EngineersQuiz 7(12 pts)March 12, 2008Turn page overĺSection:1. (3 pts) Find the length of the curve xxy2²from 1xto 2x228xxdxdy±dxxxdxxxdxxxdxxxxxdxxxdxdxdyds243.
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2. (3 pts) Find the area of the surface obtained by rotating the following curve about the x-axis: 10,ddxx2²¸¹·¨©§²y.
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Exercise: What surface is generated by this?
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3. Consider a plate occupying the region which consists of all points ´µyx,in the xy-plane where 10ddxand xydd0The areal density,G, at any point´µyx,in the given region is a function of xalone, and is given by ´ µ2g/cmxxG(a)(2 pts) Show that the mass of the plate is 2/5 g. . .
(b)(2 pts) Find the x-coordinate of the centre of mass of the plate, and give answer as a fraction.
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