Mathematics

The key insight is recognizing that "between the curve and the $y$-axis" means the horizontal distance from the parabola to the line $x = 0$. Since $x = y^2 - 4$ is always negative or zero in this interval, you're finding the area of a region bounded on the right by the $y$-axis and on the left by the parabola. Set up a horizontal strip integral: integrate the width of each strip (from the curve to the axis) with respect to $y$.

The key insight is recognizing that "between the curve and the $y$-axis" means the horizontal distance from the parabola to the line $x = 0$. Since $x = y^2 - 4$ is always negative or zero in this interval, you're finding the area of a region bounded on the right by the $y$-axis and on the left by the parabola. Set up a horizontal strip integral: integrate the width of each strip (from the curve to the axis) with respect to $y$.