How would I calculate the area of a curve given parametrically as x=4cosθ y=3sinθ?

Question

These couple questions belong to a test review that I missed from being on vacation..and have no idea how to solve. Thanks for any help!

Answer 1

use calculus

Answer 2

1. Recognize from the parametric equations, this is an ellipse.

1A. If you don't recognize it, Plot it on a graphic calculator or using a spreadsheet program (Excel) and an X-Y scatter plot.  

From the plot (or simply from the equations) recognize the curve as an ellipse with major axis radius = 4

and minor axis radius = 3

2. From the standard formula for the area of an ellipse

A = pi * a * b

A = 3.1412 * 4 * 3 = 12pi

.