oblem 12. (12.4/36) (a) We define the improper integral (over the entire plane R2) 1= fferty'dA = [ ] effy dydr = lim ffe (fry da R- Da where Da is the disk with radius a and center the origin. Show that ( ( e (+7dydx=x. (b) An equivalent definition of the improper integral in part (a) is 1 = [e (+) dA = lim [fe-(+y)dA SA where Sa is the square with vertices (ta, ta) . Use this to show that ( ex dxf ey dy = 1 . -00 (c) Deduce that [ ex dx = n . (d) By making an appropriate change of variable, show that ( ex/2dx = 27 . [This is a fundamental result for probability and statistics, specifically the normal probability distribution.]