Find the area or volume.
-$\text { Find the area between the graph of } y = \frac { 12 } { ( x - 1 ) ^ { 2 } } \text { and the } x \text {-axis, for } - \infty

Question

Find the area or volume.
-$\text { Find the area between the graph of } y = \frac { 12 } { ( x - 1 ) ^ { 2 } } \text { and the } x \text {-axis, for } - \infty < x \leq 0 \text {. }$
A) 6
B) 1
C) 12
D) 24

Quizplus · Accepted Answer

To find the area between the curve and the x-axis, we need to integrate the function with respect to x.

\begin{align*}
\int_{-\infty}^0 \frac{12}{(x-1)^2} dx &= \left[ -\frac{12}{x-1} ight]_{-\infty}^0 \
&= 12 - \lim_{x 	o -\infty} \frac{12}{x-1} \
&= 12 + 0 = 12
\end{align*}

Therefore, the area between the graph of $y=\frac{12}{(x-1)^2}$ and the x-axis, for $-\infty<x\leq0$ is 12. So the best choice is (C).

Find the Area or Volume A) 6 B) 1 C) 12 D) 24

Find the Area or Volume A) 6
B) 1
C) 12
D) 24