Volume of a rotation

[InterserveVB]

Can someone review my work and see what I am doing wrong. The correct answer is 315.73pi.

Sketch a graph to estimate the x-coordinates of the points of intersection of the given curves. Then use this information to estimate the volume of the solid obtained by rotating about the y-axis the region enclosed by the curves y=0 and y = -x^4+4x^3-x^2+4x

 

[Daniel_Feldman]

You lost the pi in your final step.

 

[galactus]

\(\displaystyle {-2}{\pi}\int_{0}^{4}{x^{2}(x^{3}-4x^{2}+x-4)}dx=\frac{4736{\pi}}{15}\)

 

[InterserveVB]

ok, I see what I did. Thx. Also, how do you type the symbols (the integration sign, etc into the forum? What software did you use to make the pic?

 

[galactus]

Use Latex to make the symbols. To see, click on quote in my post. As for the picture, I done it with Maple, exported to a gif, hosted with ImageShack and copy and pasted it in my post.