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Question
The area enclosed by the ellipse `x^2/"a"^2 + y^2/"b"^2` = 1 is equal to ______.
Options
π2ab
πab
πa2b
πab2
Solution
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.
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