Mathematics

The key is to recognize that both curves are written as functions of $y$, so integrate with respect to $y$ rather than $x$. Find where the line and parabola intersect by setting their expressions equal, then integrate the difference between the rightmost and leftmost curves over that $y$-interval. This approach avoids messy algebra and keeps the setup clean.

The key is to recognize that both curves are written as functions of $y$, so integrate with respect to $y$ rather than $x$. Find where the line and parabola intersect by setting their expressions equal, then integrate the difference between the rightmost and leftmost curves over that $y$-interval. This approach avoids messy algebra and keeps the setup clean.