Find the area or volume.
-Find the volume of the solid generated by revolving the region in the first quadrant under the curve $y = \frac { 4 } { x ^ { 2 } }$, bounded on the left by $x = 1$, about the $x$-axis.
A) $\frac { 16 } { 3 } \pi$
B) $4 \pi$
C) $\frac { 4 } { 5 } \pi$
D) $16 \pi$

Question

Quizplus · Accepted Answer

The volume of the solid generated by revolving the region under the curve $y = \frac{4}{x^2}$ from $x = 1$ to infinity about the x-axis can be found using the formula for the volume of revolution, $V = \pi \int_{a}^{b} [f(x)]^2 dx$. Here, $f(x) = \frac{4}{x^2}$, $a = 1$, and $b = \infty$. The integral simplifies to $\pi \int_{1}^{\infty} \frac{16}{x^4} dx$, which evaluates to $\frac{16}{3} \pi$, hence the correct answer is $\frac{16}{3} \pi$.

Find the Area or Volume y=4x2y = \frac { 4 } { x ^ { 2 } }y=x24​

Find the Area or Volume $y = \frac { 4 } { x ^ { 2 } }$