Vinny's Vigilant Vaccurobots (VVV) makes robot vacuums that find their own path across the floor as they sweep up dirt and dust. They are testing out their new Vuum model. VVV scatters dust on a 4-meter by 4-meter square rug. The density of the dust on the rug is given by the function D(x, y) = 0.2x2 - 0.1xy + 3 where D is measured in grams per square meter. Both a and y are measured in meters from the southwest corner of the rug, and are both in the interval [0, 4]. The Vuum takes a path described by the parametric equations (t) = 4t2 - 14 y (t ) = 4-+2 where t is in minutes since the start of the test. The test starts at t = 0 and ends at t = 2. 1. Find a formula for the density of dust the robot encounters at time t along its path. I 2. Find the average density of dust the robot encounters along its path