integral 0 menuju 1 x√9-x^2 =

[tex]
\text{Pertama, kita tentukan dulu hasil integral tak-tentunya}\\
\text{misalkan }u=9-x^2\Leftrightarrow du=-2xdx\Leftrightarrow -\frac{1}{2}du=xdx\\
\text{selanjutnya, diperoleh}\\
\int{x\sqrt{9-x^2}}dx\\
=\int{\sqrt{u}\left(-\frac{1}{2}du\right)}\\
=-\frac{1}{2}\cdot\frac{2}{3}u^{\frac{3}{2}}+c\\
=-\frac{1}{3}(9-x^2)^{\frac{3}{2}}+c\\
\\
\text{Kemudian, diperoleh}\\
\int_0^1{x\sqrt{9-x^2}}dx\\
=\begin{bmatrix}-\frac{1}{3}(9-x^2)^{\frac{3}{2}}\end{bmatrix}_0^1\\
=-\frac{1}{3}(9-1^2)^{\frac{3}{2}}-\left(-\frac{1}{3}(9-0^2)^{\frac{3}{2}}\right)\\
=-\frac{1}{3}\cdot8^{\frac{3}{2}}+\frac{1}{3}\cdot9^{\frac{3}{2}}\\
=\frac{1}{3}\left(-2^{\frac{9}{2}}+3^{\frac{6}{2}}\right)\\
=\frac{1}{3}\left(-16\sqrt{2}+27\right)
[/tex]