the curves x = -1/(y² - 5) and x = 1 are graphed. which expression represents the area bounded by the…

Explanation:

Step1: Determine the formula for area between curves

When finding the area between two curves $x = f(y)$ and $x = g(y)$ with $f(y)\geq g(y)$ over the interval $[a,b]$, the area $A=\int_{a}^{b}(f(y)-g(y))dy$. Here, the right - hand curve is $x = 1$ and the left - hand curve is $x=-\frac{1}{y^{2}-5}$, so $f(y)=1$ and $g(y)=-\frac{1}{y^{2}-5}$.

Step2: Find the intersection points in the y - axis

To find the limits of integration, we set the two $x$ - values equal: $-\frac{1}{y^{2}-5}=1$. Cross - multiply to get $- 1=y^{2}-5$, then $y^{2}=4$, so $y=-2$ and $y = 2$. These are the limits of integration for $y$.

Step3: Set up the integral

The area $A=\int_{-2}^{2}(1-(-\frac{1}{y^{2}-5}))dy=\int_{-2}^{2}(1 + \frac{1}{y^{2}-5})dy$.

Answer:

B. $\int_{-2}^{2}(1+\frac{1}{y^{2}-5})dy$