Chapter 10.3, Problem 85E

Areas of Simple Closed Curves In Exercises 81-86, use a computer algebra system and the result of Exercise 77 to match the closed curse with its area. (These exercises were based on “The Surveyor’s Area Formula'’ by Bart Braden, College Mathematics Journal, September 1986, pp. 335-337, by permission of the author.)

(a) $\frac{8}{3}ab$

(b) $\frac{3}{8}\pi a^2$

(c) $2\pi a^2$

(d) $\pi ab$

(e) $2\pi ab$

(f) $6\pi a^2$

Hourglass: $(0\le t\le 2\pi )$

$\begin{array}{l}x=a\sin 2t\\ y=b\sin t\end{array}$