Expression for volume of solid of rotation

[theschaef]

The question is to find an expression for the volume, but not evalute of..

the area between the curves y=x and y=4x-x^2, rotated about the line x=7

I got V = integral {11 to 14} [ 2pi (x-7)(3x-x^2) ]

does someone want to try this and see what they get... im just unsure of my answer

 

[galactus]

If we set \(\displaystyle \L\\x=4x-x^{2}\),

We find x=0 and x=3.

Using 'shells':

\(\displaystyle \L\\2{\pi}\int_{0}^{3}(x-7)(x-(4x-x^{2}))dx\)

\(\displaystyle \L\\2{\pi}\int_{0}^{3}(x^{3}-10x^{2}+21x)dx\)