Volume Help (1 Viewer)

[Blackmancan]

Find the volume of the solid of revolution formed if the area enclosed between the curves y=x^2 and y=(x-2)^2 is rotated about the x-axis.
The answer is 2pi/5 but I keep getting something different :/
Thanks in advance

 

[zeebobDD]

well you want to split up the integrals, after finding the intersection as 2

integral, 0 to 1 of x^4 dx will give you the first bit of the volume

then integral 1 to 2 of (x-2)^4 dx will give you the other bit,

will be PI [x^5/5] 1 to 0 which is PI/5 +

PI[(x-2)^5/5] 1 to 2, which will give you PI/5, therefore both integrals added will give you 2pi/5

 

[Drongoski]

Find the volume of the solid of revolution formed if the area enclosed between the curves y=x^2 and y=(x-2)^2 is rotated about the x-axis.
The answer is 2pi/5 but I keep getting something different :/
Thanks in advance

The 2 parabolae intersect at x=1

.: Volume V = V1 + V2





Very much what zeebob indicated.