7. Use your knowledge of ellipses and their areas to evaluate the following integral. 2 + y = - 2 a. Area(upper half of an ellipse) = 22 1dx Change the above integral in x to an integral in u. Hint: Use the substitution x = 2sin(u) b. Evaluate the integral in terms of u. 0 2 -~ c. The area of a total ellipse is A = ab, where a and b are the semi-major and semi- minor axes. What is a? What is b? What is the total area of the ellipse? d. Are your answers from (b) and (c) compatible? (yes or no)