QPaperGen

The area (\(A\)) of the region enclosed by the curve \(y = f(x)\), the \(x\)-axis, and the vertical lines \(x=a\) and \(x=b\) is given by the definite integral:\[A = \int_{a}^{b} f(x) dx\]
\[A = \int_{0}^{4} x^{1/2} dx\]
\[A = \frac{2}{3} \left[ x^{3/2} \right]_{0}^{4}\]
\[A = \frac{2}{3} \left[ (4)^{3/2} - (0)^{3/2} \right]\]
\[A = \frac{16}{3}\]