Which of the following integrals represents the volume of the solid obtained by rotating the region bounded by the curves $y=x^4$ and $y=\sin(\frac{\pi x}{2})$ about the line $x=-8\,?$

A. $\displaystyle \int_{0}^{\,1} {2 \pi (8 - x) \left(x^4-\sin\left(\frac{\pi x}{2}\right)\right)}\,dx$
B. $\displaystyle \int_{0}^{\,1} {2 \pi (x + 8) \left(\sin\left(\frac{\pi x}{2}\right)-x^4\right)}\,dx$
C. $\displaystyle \int_{0}^{\,1} {2 \pi (x - 8) \left(x^4-\sin\left(\frac{\pi x}{2}\right)\right)}\,dx$
D. $\displaystyle \int_{0}^{\,1} {2 \pi (x - 8) \left(\sin\left(\frac{\pi x}{2}\right)-x^4\right)}\,dx$
E. $\displaystyle \int_{0}^{\,1} {2 \pi (8 - x) \left(\sin\left(\frac{\pi x}{2}\right)-x^4\right)}\,dx$
F. $\displaystyle \int_{0}^{\,1} {2 \pi (x + 8) \left(x^4-\sin\left(\frac{\pi x}{2}\right)\right)}\,dx$