Question

Using the definite integration area of the circle x² + y² = 25 is ______.

Answer 1

Using the definite integration area of the circle x² + y² = 25 is 25 π sq. units.

Explanation:

Given, x² + y² = 25

∴ y = `sqrt (25 - x^2)`

Area = `2 xx int_(-5)^5 sqrt(25 - x^2) dx`

Standard formula is:

`int_(-a)^a sqrt(a^2 - x^2) dx = (pi (a)^2)/2`

Putting a = 5 in the above equation, we get

`int_(-5)^5 sqrt(5^2 - x^2) dx = (pi (5)^2)/2 = (25 pi)/2`

Area = `2 xx (25 pi)/2`

= 25 π