The region R enclosed by the curves and is rotated about the line y=7. Use cylindrical shells to find the volume of the resulting solid.
$\displaystyle x = 4y-29$
$\displaystyle x = (y-8)^2 + 3$
$\displaystyle 4y-29 = (y-8)^2 + 3$
$\displaystyle 0 = y^2 - 20y + 96$
$\displaystyle 0 = (y - 8)(y - 12)$
$\displaystyle y = 8$ ... $\displaystyle y = 12$
$\displaystyle V = 2\pi \int_8^{12} (y-7)[(4y-29) - ((y-8)^2 + 3)] \, dy$