Question

The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method.

y = 10, y = x + 16/x, about the x = −2

Answer 1

Is the second curve \(y=x+\dfrac{16}{x}\) or \(y=\dfrac{x+16}{x}\)?

Answer 2

The second curve is \[y=x+\frac{ 16 }{ x }\]

Answer 3

Here's a rough sketch of the desired region:

Now, I don't know exactly where the two curves intersect, but you could show that easily with some algebra:
\[\begin{align*}x+\frac{16}{x}&=10\\
x^2-10x+16&=0\\
(x-8)(x-2)&=0\\
x&=2,~8
\end{align*}\]