I need only the answer for the (3) question and all the parts in question(3) which is (a, b, c, d, e)

Math 250 ' \\ssignment 2 s 1 6v 1 a 6v 1. (16 points) Evaluate the integral ] f ' dydx = f f \" dxdy, using either order of n 0 . o 0 {17+}: \"ix-+32 As part of the Reection on this problem, let me know if you had a reason why you chose the order that you did. Does one way turn out to be easier than the other? integration. l x 2. (22 points) Consider the integral / / dydx. 0 0 l t M2 -ly2 (a) Sketch the region in the xy-plane that we are integrating over in this problem. (b) You should have found in part (a) that the line x = 1 forms part of the boundary of your region. Find the polar coordinate equation for this line. (Hint: The answer is r 2 sec 6, so just show your work to get there from x = 1. It takes just a couple of steps.) (c) Explain why the integral is improper. (I mean an improper integral like in Calc 1] (section 8.9 of our textbook), only we have more independent variables.) ((1) Go ahead and evaluate the integral by rst convening it to polar coordinates. You should nd that this conversion lets us \"dodge" the improperness, and we can evalaute it correctly this way. (It's okay if you don't remember the antiderivative of secr. You can look it up.) 3. (34 points) Let D be the solid in the rst octant bounded by the cone z = 1/ 3(Jt2 +y2) and the cylinder x2 +y2 = 1. (Our volume lives inside the cylinder. and under the cone.) For (a), (b), and (c), set up the integral/f] MW in each of the following coordinate systems. As part I) of the problem, explain how you obtain your limits of integration for x. y. z, tit, and p. (a) Cylindrical (b) Spherical (c) Rectangular (d) Find the volume of D '_ (e) Find 2 (which is the z-coordinate of the center of mass), assuming constant density. As part of this, you'll want to evaluate one of your integrals in (a), (b), or (c)