7. (28 points) The density of insects at distance 7' meters from a small pond is given by m(r) = 1+595r2 insects per square meter. Suppose that we are trying to compute the total number of insects within 100 meters of the center of the pond. (a) We start by dividing the 100 meter radius into ve concentric rings of equal thickness. Draw a picture of this, and label Ar on the outer ring. Also label each ring using its outer radius (e. g. the outermost ring should be labeled 100m). Shade in the third ring, and use its outer radius to show that its area is approximately 24007r m2. (b) Using the right hand of the third ring (aka its outer radius), show that there are approximately 4170 insects in that ring. (c) Suppose now that we divide the circle into n concentric rings. Write down a Riemann sum approximating the total number of insects within 100 meters of the center of the pond. (d) By converting your Riemann sum into an integral, compute the total number of insects within 100 meters of the center of the pool