What is the area of the region in the first quadrant between the circle $x^{2} + y^{2} = 16$ and the line $x + y = 4$?

Explanation

1. 01

   Quarter circle minus the triangle under the line: $\int_0^{4} \left(\sqrt{16 - x^{2}} - (4 - x)\right)dx$.

2. 02

   $4\pi - \frac{1}{2} \times 4 \times 4 = 4\pi - 8$ square units.