Mathematics

The key is recognizing that you're finding the area trapped between a downward-opening parabola and the axes in the first quadrant. First, identify where the parabola intersects the $x$-axis (where $y=0$), which gives you the right boundary of your region. Then set up a definite integral with respect to $x$ from $0$ to that intersection point, integrating the parabola's height. This is a straightforward application of the fundamental theorem: area equals the antiderivative evaluated at the bounds.

The key is recognizing that you're finding the area trapped between a downward-opening parabola and the axes in the first quadrant. First, identify where the parabola intersects the $x$-axis (where $y=0$), which gives you the right boundary of your region. Then set up a definite integral with respect to $x$ from $0$ to that intersection point, integrating the parabola's height. This is a straightforward application of the fundamental theorem: area equals the antiderivative evaluated at the bounds.