00:01
Hi, in this question, given that the function f of x equals x and g of x equals x square by 4 between x equals 1 and x equals 2, rotation about the x -axis, we have to find the volume of the region.
00:21
We know that the volume v equals integral over a to b pi into f of x minus d the whole square minus g of x minus d the whole square into dx.
00:40
So here, rotation about x -axis, so we have to consider y equals 0, that is d equals 0.
00:49
Hence, the volume v can be written as integral over 1 to 2 pi into f of x is x minus 0 the whole square minus g of x is x square by 4 minus 0 the whole square into dx.
01:04
On further simplifying, we get pi is constant, so out of the integral, limit varies from 1 to 2, here x square minus x power 4 divided by 16 into dx.
01:19
On integrating, then we get pi into x cube divided by 3 minus x power 5 divided by 80...