Using integration, find the area of the following region: {(x, y): |x - 1| ≤ y ≤ √(5 - x^2)}

Question

Using integration, find the area of the following region:

{(x, y): |x - 1| ≤ y ≤ \(\sqrt{5-x^2}\)}

Answer 1

We have provided

{(x, y): |x - 1| ≤ y ≤ \(\sqrt{5-x^2}\)}

Equation of curve is y = \(\sqrt{5-x^2}\) or \(y^2+x^2=5\), which is a circle with centre at (0, 0) and radius \(\frac 52\).

Equation of line is y = |x - 1|

Consider, y = x - 1 and y = \(\sqrt{5-x^2}\)

Eliminating y, we get

The required area is