Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

Question

y = 4 − 1/2x, y = 0, x = 0, x = 1; about the x-axis

V = ????

Answer 1

think of discs with radius y, thickness dx, so

v = ∫[0,1] πy^2 dx
= π∫[0,1] (4-x/2)^2 dx
a nice easy integral. You should get 169/12 π