Find the area or volume.
-$\text { Find the area of the region bounded by the curve } y = 8 x ^ { - 2 } \text {, the } x \text {-axis, and on the left by } x = 1 \text {. }$
A) 64
B) 16
C) 8
D) 4

Question

Quizplus · Accepted Answer

To find the area, we need to integrate the function with respect to x between the bounds 1 and infinity (since the curve extends infinitely in both directions along the x-axis).
\begin{align*}
	ext{Area} &= \int_1^{\infty} 8x^{-2} \,dx \
&= \lim_{t	o\infty} \int_1^{t} 8x^{-2} \,dx \
&= \lim_{t	o\infty} \left[-8x^{-1}ight]_1^t \
&= \lim_{t	o\infty} [-8t^{-1}+8] \
&= 8
\end{align*}
Therefore, the area is 8 units squared.