00:01
Hi, in this question we are given with the equations as y is equal to x squared plus two, y is equals to minus x squared plus 2x plus 6, x is equal to 0 and x is equal to 3.
00:14
Here, using these equations we will be having a region.
00:18
As we can see from this graph, we are having a region between this part and this part from x is equal to 0 to x is equal to 3.
00:30
And we need to find the volume of the solid that is generated by revolving this region about the x -exes.
00:39
And here, first we find the intersection point as equating both the equations, we get x -square plus 2 is equals to minus x -square plus 2x plus 6.
00:50
And solving this further, we get 2x -square minus 2x minus 4 is equal to 0.
00:56
Or we get x squared minus x minus 2 is equals to 0 and solving this further we get a value for x as equal to 2 and putting this value we get y as equals to 2 square plus 2 that is equal to 6 so we have the intersection point as 2 6 now we can find the volume that will be equals to pi times integration from a to b are 2 square dx minus pi integration from a to b are 1 square dx...