7. Use your knowledge of ellipses and their areas to evaluate the following integral. 2 +...

Transcribed Image Text:

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) 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)