Finding the Area of an Ellipse in Calculus III

[shinobi12]

Homework Statement

Find the area of the ellipse (x^2)/4 + (y^2)/9 = 1

Homework Equations

(1/2) * Integral of xdy - ydx = area of a Region

The Attempt at a Solution

The problem is weird to me because its complicated to attempt it in rectangular or polar coordinates)

 

[Mark44]

How is the equation you give in #2 relevant to this problem? It's possible that it is, but if so, you'll need to refresh my memory as to why that's so. Also, you'll need a definite integral, with limits of integration.

The way I would approach this problem is to solve for y (the positive solution) and integrate from x = 0 to x = 2. That number would be 1/4 of the area inside the ellipse.

 

[Defennder]

Well since the title of the thread is calc 3, I guess this means you have learned about double integrals already. Evaluate $$\iint dA$$ for that region to get the area.