Determine the area under the curve included between the lines x = 0 and x = a

Squaring both sides

⇒ y² = a² - x²

⇒ x² + y² = a²

This is equation of circle having center as (0, 0) and radius a

Now in -a ≤ x ≤ a and y ≥ 0 which means x and y both positive or x negative and y positive hence the curve has to be above X-axis in 1^st and 2^nd quadrant

x = 0 is equation of Y-axis and x = a is a line parallel to Y-axis passing through (a, 0)

So we have to integrate from 0 to a

let us find area under curve

Integrate from 0 to a

Using uv rule of integration where u and v are functions of x

Here and v = 1

Hence

But

We know that

Hence area bounded = unit²