\(\int^9_0 \sqrt{x} dx\)

\(\frac{x^{\frac{1}{2}} + 1}{\frac{1}{2} + 1}\) |\(^9_0\)

\(\frac{2x^{\frac{3}{2}}}{3}\)|\(^9_0\)

= \(\frac{2(9)^{\frac{3}{2}}}{3}\)

= \(\frac{2(3)^3}{3}\)

= \(\frac{2 \times 27}{3}\)

= 2 x 9

= 18