The goal of this problem is to find a general formula for the area of an ellipse in terms of the lengths of its semi-major and semi-minor axes (denoted by a and b in the figure below). (a) The equation of the ellipse pictured is + Show that the equation for the portion of the ellipse in the first quadrant is y= a-x. (b) Write down and evaluate an integral for the area of the shaded region. (c) What is the area of the ellipse in terms of a and b?