Problem $2$: $20pts$ The region $R$ shaded below is bounded by $x^2+y^2=8$ and $y=x^2.$

Exhibit an integral or sum of integrals that would represent the perimeter of the boundary of region $R.$

For each integral you write down, explain $($via a complete English sentence or by labeling the graph$)$ which part of the perimeter it computes.

If you utilize symmetry when finding the perimeter, make sure to explain how you used it$.$

Use technology to calculate the perimeter to $3$ decimal places.

You may utilize computational technology $($not AI$)$ to do this problem in any way you would like $($finding intersection points, derivatives, integrals, etc$).$ Make sure to state what you are computing, what you use to perform calculations, and report your final answer to $3$ decimal places.