Fully answers and clear explanation

l x 2. (22 points) Consider the integral / / dydx. 0 0 1 1M2 + y2 (a) Sketch the region in the xy-plane that we are integrating over in this problem. (b) You should have found in pan (a) that the line x = 1 forms pan of the boundary of your region. Find the polar coordinate equation for this line. (Hint: The answer is r = sect), so just show your work to get there from x = 1. It takes just a couple of steps.) ((3) Explain why the integral is improper. (I mean an improper integral like in Calc 11 (section 8.9 of our textbook), only we have more independent variables.) ((1) Go ahead and evaluate the integral by rst converting it to polar coordinates. You should nd that this conversion lets us \"dodge\" the improperness, and we can evalaule it correctly this way. (It's okay if you don't remember the antiderivative of sect. You can look it up.)