Mathematics

The key is recognizing that when one curve is written as $x$ in terms of $y$, it's often easier to integrate with respect to $y$ rather than $x$. Find where the parabola and line intersect by setting them equal, then determine which curve is to the right. The area between them is $\int (x_{\text{right}} - x_{\text{left}}) \, dy$ over your interval—this avoids messy inverse functions and gives you a clean calculation.

The key is recognizing that when one curve is written as $x$ in terms of $y$, it's often easier to integrate with respect to $y$ rather than $x$. Find where the parabola and line intersect by setting them equal, then determine which curve is to the right. The area between them is $\int (x_{\text{right}} - x_{\text{left}}) \, dy$ over your interval—this avoids messy inverse functions and gives you a clean calculation.