Volume of Solid in Calculus Find the volume of the solid whose base is the region in the first quadrant bounded by $y=x^5, y=1$ and the $y$-axis and whose cross sections perpeddicular to the $x$ axis are semicircles
I am tutoring someone, and we keep getting the wrong answer, any help would be appreciated

The diameter of the semicircular slice is $1 - x^5$, and its area then is $\pi(1-x^5)^2/8.$
The curve $y=x^5$ intersects the line $y=1$ at $x=1$ in the first quadrant, so your limits of integration are $[0,1]$.
Then, your infinitesimal slice has volume $(\pi(1-x^5)^2/8) dx$, and the volume then is
$$V = \frac{\pi}{8} \int_0^1 (1-x^5)^2 dx = \left.\frac{\pi}{8}(x - \frac{1}{3}x^6 + \frac{1}{11}x^{11})\right|_0^1 = \frac{25 \pi}{264}.$$ 
