[SPLIT] vol. of solid: y=3x^2 and y=1 about y=1

[Pre]

Find the volume of the solid formed by rotating the region bounded by y=3x^2 and y=1 about y=1.

And I know even for me this seems really easy but I keep getting a small answer less that 1.

I put the integral from -.577 to .577 of (1-3x^2)^2

Then square it to get (1-6x^2+9x^4)dx and anti diferentiate to get pi[x-2x^3+(9/5)^5] I know I'm doing something wrong I just dont know what because I got .616pi which seems really small.

 

[skeeter]

what happens when you square or cube a number less than 1 ? Don't you end up with a value smaller than what you started with? That's why the numbers are small.

btw ... don't bother squaring (1 - 3x²), just type it into your calculator as is ...

\(\displaystyle \L V = 2\pi \int_0^{.577} (1 - 3x^2)^2 dx \approx 1.935\)