Question

(10 marks) Let C be the curve 64x – - y3 = 0 between y = 0 and y = 3. Sketch the graph of this curve. In each part, set up, but do not evaluate, an integral or a sum of integrals that solves the problem. (a) Find the area of the surface generated by revolving C about the x-axis by integrating with respect to x. (b) Find the area of the surface generated by revolving C about the y-axis by integrating with respect to y. (C) Find the area of the surface generated by revolving C about the line y=-2 by integrating with respect to y.

Answer 1

•Y=8- we have to find the area of the surface generated by revolving c about n-anis. 2x y20 y3 = 640 required generated surface area Sal y 2=6. + As je dne 1=9 43=644 so = 641 = uzo 43=64h. 2 (3)3 = 6th 2012 2) 64 osus 21 y3=641- 342 19E (648813=4 xls 3y2 do 64 dy 64. an dy an) 344 it dy. 12= 1+ (392) 164. ? le 3 (44 1314 (an 21/64 2 dn area=28 4 se's V 14/64 (3 16 4²13) 27/64 /*/4 3223) Men's relea 1 4913 an 2204 0

NOM, we tind the area generated by have to of the surface revolving about s-anis ci Y364x=0 required generated surface yab Szive upite dy. y area y=9 -> Os 453 y3 = 6.9K 342 = 64 dn dy. a dh ly = 342 64 (642 Vit (* = /user - vit gozel forma part de os ver og S S.AZ x گرو it ose dy Au we have to surface area find the generated when revolve the the line y = -2 about 437 curve required S.A. 17.994 dys =fuse (*+2) Shtetet A 925 Joris-W), *19-45 >>។ Here &=-2, 920, 6=3.
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