Calculus $2$: Integration Problem Where You Find the Volume of a Rotating Object

Question

I solved the following problem but my solution doesn't match the answer on my math worksheet.

Problem: Find the area of the region bounded by the curve $y = 7x^{-2}$, the $x$-axis, and on the left by $x = 1$.

Below is my solution: Am I correct? If not, please let me know where I went wrong.

My Answer: $\dfrac{49\pi}{3}$. Worksheet Answer: $7$.

Answer 1

The area is simply $$A = \int_{x=1}^\infty ydx$$

So,

$$A = \int_1^{\infty}7x^{-2}dx = \left[\frac{-7}{x}\right]^\infty_1 = (-0+7) = 7$$

Answer 2

The question you've given in bold doesn't mention anything about the volume of a rotating object. That may be in a later part of the question. The answer to the question you've given is...

$$ \int_1^\infty 7x^{-2}dx = \left[-\frac{7}{x}\right]_1^{\infty} = 7.$$