1. (10 points} Consider the integral if rzydA, where R is the region bounded by the tunes 3; = 0, y = 2:3, and y = 1M: + 3, shown below. Set up the integral with dA = drdy and as dd = dydx. Evaluate whichever order you 1would like. 2. (a) {5 points) How can double integrals be used to compute the area of a region? \\Vhy does this work? (b) {Iii points} Sketch the region R in the rst quadrant between the circles ..":2+',r2 = 15 and ..".2+{g,iI2:I2 = 4, and use a doubie integral to nd the area of this region. Hint: use polar coordinates. 3. Consider the \"ice cream cone" between the sphere of radius 4 centered at the origin, and the cone that is g up from the aypiane. [Recall that in Cartesian coordinates, this cone can be described as 2; 2 J31 {1:2 + 3F} (a) (2 points) Sketch a side View and a. top View of the \"ice cream cone." Label appropriately. (b) [4 points) Set up, but do not evaluate, an integral in Cartesian coordinates describing the volume of the \"ice cream cone.\" (c) {-1 points) Set up, but do not evaluate, an integral in cylindrical coordinates describing the volume of the \"ice cream cone.\" (d) {4 points] Set up, but do not evaluate, an integral in spherical coordinates dcribing the volume of the l'ice cream cone.\