The formula to find the volume is:
That means "a" would be setup as follows:
The integral will be from 0 to 1.
The reason we multiply it by 2 is because the two lines actually form a solid twice. Therefore we will take the integral from a point of intersection to the next point of intersection on one solid and multiply times 2 in order to get the volume of both solids.
b)To find the area going around the y-axis we need to place all of our 's in terms of .
We come out with and . Remember the graph looks the same, but the equations are just in terms of .
Then just use the formula to find the volume.
Your setup should look as follows:
The integral will be from 0 to 1 again because the graphs intersect at those points.
Question "c" is beyond my knowledge. Maybe someone else here can enlighten me.
If you have any questions, just ask!