"The region enclosed by the curves $\displaystyle y=x^{3}$ and $\displaystyle y=\sqrt{x}$ is roated about the line $\displaystyle x=1$. Fint the volume of the resulting solid" -James Stewart

answer:$\displaystyle \frac{13\pi}{30}$

what I did:

difference of shells formula is $\displaystyle 2\pi \int x(f(x)-g(x))$

so in this problem $\displaystyle f(x)=\sqrt{x}$ and $\displaystyle g(x)=x^3$. The intersections are $\displaystyle x=0,1$. I get confused because it's not being rotated around the y-axis but $\displaystyle x=1$

I tried $\displaystyle V= 2 \pi \int_0^1 x((1-\sqrt{x})-(1-x^{3})$ but I end up with a negative number.