Find the area of the ellipse x^2/25 + y^2/16

Question

Find the area of the ellipse  \(\cfrac{x^2}{25}+\cfrac{y^2}{16} =1\) using integration.

Answer 1

By the symmetry of the ellipse, its area is equal to 4 times the area of the region OABO. Clearly, for this region, the limits of integration are 0 and 5.

From the equation of the ellipse

In the first quadrant y > 0

∴ area of the ellipse = 4(area of the region OABO)