Answer
\[
\int_{1}^{4} 3 \sqrt{x} d x=14
\]
Work Step by Step
The area under the curve $f(x)=3 \sqrt{x}$ over the interval [1,4] is $\int_{1}^{4} 3 \sqrt{x} d x$
\[
\begin{aligned}
\int_{1}^{4} 3 \sqrt{x} d x &=3 \int_{1}^{4} x^{\frac{1}{2}} d x \\
&=\left. \frac{2 x^{\frac{3}{2}}}{3} \cdot 3\right|_{1} ^{4} \\
&=[-\sqrt{1}+\sqrt{4^{3}}]2 \\
&=14
\end{aligned}
\]
