Question

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Find the area of the surface obtained by rotating the curve y = 6 - X , os x 62 arond x-axis

Answer 1

Find the area of the surface obtained by rotating the curve y = 6 - X , os x 42 arond x-axis The area of the surface of revolution for y = f(x) from x = a to x = b about the y-axis is: y (2, 4.667) S=22*111+8"(x)? dx. Here, we have dy/dx = -27/3 for region Re for resim Ry Surface area is estorst surface area t=0 of cylinder with radius 2 units & height 14/3 units. So, we have Szza P²2 / +(24/72 dx + 22 (2) x 18 25 x S9+ 4x2) dx + soal We have fx Vo-As? dr = 125 vu du Apply u- substitution: u = 9+48? => Si Vu du = 3 outdu 9 Therefore, SóxV9 = 48% dx = 3..0 = 495 Hence, the surface area is: S = 491 – 567 = 497 – 1887 – 2171 9