Question
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = 4 − 1/2x, y = 0, x = 0, x = 1; about the x-axis
V = ????
y = 4 − 1/2x, y = 0, x = 0, x = 1; about the x-axis
V = ????
Answers
Steve
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
v = ∫[0,1] πy^2 dx
= π∫[0,1] (4-x/2)^2 dx
a nice easy integral. You should get 169/12 π