Use integration and trigonometric substitution to find the area

Question

Use integration and trigonometric substitution to find the area enclosed by the ellipse: x^2/36 + y^2/16 = 1.

Answer 1

First do a little algebra to get y as a function of x as y=(2/3)sqrt(36-x²)

Then make the substitution x=6 sin θ to evaluate the integral.

Find the integral from 0 to 6 which is the area of (1/4) of the ellipse.