Question

The density at each point of a 1 centimeter square (i.e., each side has length 1 centimeter) microchip is 4 + r² grams per square centimeter, where r is the distance in centimeters from the point to the center of the chip. What is the mass of the chip?

Answer 1

We model the chip as the rectangle

Then the center is the point (0, 0) and the squared distance of a point (x, y) to the center is r² = x² + y² . Thus the mass m can be computed as