All changes saved

Answer the following question. After working through the problem on a separate sheet of paper, transfer the information as best you can into the text box below and click "Scoring Guidelines"

Consider the functions $f(x)=\frac{10ln(2)}{2x+3}$ and $g(x)=se{c}^2(x)tan(x)$ which are graphed in the given figure. Let $R$ be the shaded region shown in the figure that is bounded by $f(x),g(x)$ and the $y-$axis. The curves $f(x)$ and $g(x)$ intersect at the point $(0\mathrm{.}465,0\mathrm{.}628)$

a$)$ Calculate ${\displaystyle \underset{0}{\overset{}{}}}f(x)dx$ or explain why it diverges. Show the work that leads to your answer.

b$)$ Write, but do not evaluate, an expression for the volume of the solid generated by rotating the region $R$ about the horizontal line $y=-1.$

c$)$ Calculate ${\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}g(x)dx$ or explain why it diverges. Show the work that leads to your answer.