2. Recall our old friend the curve C in Cartesian form defined by C = {(I, y) ER' [ x' + 4y = 4y' ). In this problem we aim to find the area A bounded by C. As you have seen from previous assignments, @ is symmetric with respect to both the z-axis and the y-axis. Thus the key step is to find the area A' bounded by C that is in the first quadrant (i.e., in {(r, y) ( R'|x 2 0, y 2 0}). Follow the steps below to find the areas A' and A. (a) Explain why the area A' is equal to where g(y) = 2y* V/1 - yz.(b) We now use integration by substitution to convert the definite integral in (2a) into the one you solved in WebWork Problem 2. As above, we define g(y) = 2y v1 -y?. (i) Use the integration by substitution rule in the definite integral form given on Slide 471 to show that: A' = g(sin(y)) sin'(y) dy (ii) Use the Pythagorean identity to express the integrand g(sin(y)) sin'(y) from (i) in the form you solved in WebWork Problem 2. Be careful to explain any choices you make about the sign of factors.(c) Find the area A'. (d) Using symmetry and part (2c), find the area A enclosed by the curve C