The area bounded by the curve and line is rotated around the y-axis. What is the volume of the resulting structure?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
Such problems can be solved with the general formula:
V o l u m e = 2 π ∫ a b x f ( x ) d x
Factorising shows that the region in question is between x=0 and x=2, hence a = 0 and b = 2 .
Therefore:
V o l u m e = 2 π ∫ 0 2 x ( 2 x 2 − x 3 ) d x = 5 1 6 π