I'm supposed to determine the volume of the region obtained by revolving the region lying below the graph of the given function and above the $x$-axis about the specified axis. The problem I'm given is
$y = x^2 + x + 1,\quad y = 10,\quad x \text{ in } [0, 2]$.
I drew it out. We are using the Washer method here. So big $R$ is $10$, little $r$ is $x^2+x+1$.
So now it's just a matter of plugging in the numbers and doing the integration.
$$\pi \int_0^2 (10)^2 - (x^2+x+1)^2\ dx,$$
Problem is, I get $\dfrac{858\pi}{5}$ but according to the book, the answer is $\dfrac{1574\pi}{15}$. I can't figure out what I am doing wrong. Help appreciated.
the correct formula is $$ \pi \int_0^2 \left(100- \left(10 -x^2-x-1\right)^2\right)\ dx.$$