The area bounded by the graphs \[y=\sqrt{2-x^2} \qquad \text{and} \qquad x+\left(\sqrt{2}-1\right)y=\sqrt{2}\] equals

  1. \(\dfrac{\sin{\sqrt{2}}}{\sqrt{2}}\);

  2. \(\dfrac{\pi}{4}-\dfrac{1}{\sqrt{2}}\);

  3. \(\dfrac{\pi}{2\sqrt{2}}\);

  4. \(\dfrac{\pi^2}{6}\).

Could we start by sketching the graphs of our two functions?

How do we calculate the area of the required shape? Could we write it as the difference of two other areas?

What would we expect our answer to look like? Do some of the options in the list seem more likely than others?