5. Graphical Applications of Derivatives

Find the exact length of the curve $y=\frac{x^3}{3}+\frac{1}{4x}$ for $1\le x\le 3$.

Find the length of the loop of the curve given by $x=6t-2t^3$, $y=6t^2$.

Use symmetry to evaluate the double integral of $f(x,y)=xy$ over the region $R$, where $R$ is the disk $x^2+y^2\le 4$.

Which of the following best describes the end behavior of the function $f\left(x\right)=2x^3-3x^2-3$?