this question is designed to be answered with a calculator. region r is bounded by the functions $f(x)=log…

this question is designed to be answered with a calculator. region r is bounded by the functions $f(x)=log x$ and $g(x)=\frac{1}{9}(x^{2}-10x + 9)$. which statement describes the area of region r? the area is approximately 14.595. the area is approximately 15.091. the area is approximately 15.573. the area cannot be found as $lim_{x\rightarrow0}f(x)=-infty$.

this question is designed to be answered with a calculator. region r is bounded by the functions $f(x)=log x$ and $g(x)=\frac{1}{9}(x^{2}-10x + 9)$. which statement describes the area of region r? the area is approximately 14.595. the area is approximately 15.091. the area is approximately 15.573. the area cannot be found as $lim_{x\rightarrow0}f(x)=-infty$.

Answer

Explanation:

Step1: Find intersection points

Set $\log x=\frac{1}{9}(x^{2}-10x + 9)$. Use a calculator to find the intersection points of the two curves. Let the lower - bound be $a$ and the upper - bound be $b$.

Step2: Set up area formula

The area $A$ between two curves $y = f(x)$ and $y = g(x)$ is given by $A=\int_{a}^{b}|f(x)-g(x)|dx$. Here, $A=\int_{a}^{b}\left|\log x-\frac{1}{9}(x^{2}-10x + 9)\right|dx$.

Step3: Evaluate integral

Use a calculator to evaluate the definite integral $\int_{a}^{b}\left|\log x-\frac{1}{9}(x^{2}-10x + 9)\right|dx$. The result is approximately $15.091$.

Answer:

The area is approximately 15.091.