Question

Ok the attached image is from a calculus textbook (http://www.stewartcalculus.com/media/11_home.php).

The question is simple enough -- it says that this figure contains all points inside the square that are closer to the center than to the sides of the square. Find the area of this region.

Anyone have an idea on how to get started?

The image will be uploaded shortly.

Answer 1

I think, you'll need to do 2 integrals, and then using symmetry you should be able to apply these to the rest of the diagram. However, I'm not sure of the best way to set up the integrals.
This picture very roughly imitates your shape. The areas I've shaded need to be integrated, each one separately. The area on the left you can find by looking at the center of the square and the left side of the box. The area in the middle can be found by looking at the center of the square and the upper part of the square. You just need to find the equation of the line that is equidistant from the corresponding sides of the square and the center of the square. If I remember correctly, these should take the form of hyperbolas.