Question

The area enclosed by the ellipse `x^2/"a"^2 + y^2/"b"^2` = 1 is equal to ______.

Options

• π²ab

• πab

• πa²b

• πab²

Answer 1

The area enclosed by the ellipse `x^2/"a"^2 + y^2/"b"^2` = 1 is equal to πab.

Explanation:

Since Area = `4 int_0^"a"  "b"/"a" sqrt("a"^2 - x^2)  "d"x`

= `(4"b")/"a"[x/2 sqrt("a"^2 - x^2) + "a"^2/2 + "a"^2/2 sin^-1  x/"a"]_0^"a"`

= πab.