Please help me with my final Calculus assignment!

Question

Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep safe. Since Dr. Jones is a mathematician, she suggests building fences described by  and . Farmer Jones thinks this would be much harder than just building an enclosure with straight sides, but he wants to please his wife. What is the area of the enclosed region?

Answer 1

Since this is your last assignment, I will not work the whole problem for you but I will tell you how to do it.

First and most important (and if you have not learned this lesson by now, then learn it now): DRAW A FIGURE!

Where do the two equations intersect? 5x² = x² + 9 => x = ±3/2.

The area is symmetric about the y-axis.

The area you want then is 2 times the integral from 0 to 3/2 of x²+9-5x^2.

^{You should be able to get it from here.}