The region inside the circle $x^{2} + y^{2} = 10$ and above the line $y = 1$ is found with vertical strips. Between which limits of $x$ is the integral taken?

Explanation

1. 01

   The line meets the circle where $x^{2} + 1 = 10$, so $x = \pm 3$.

2. 02

   Between them each strip runs from $y = 1$ up to $y = \sqrt{10 - x^{2}}$: $\int_{-3}^{3} \left(\sqrt{10 - x^{2}} - 1\right)dx$.