[tex]\int\limits_{0}^{3/2}[x^{2}]dx[/tex]

[Гост]

[tex]\int\limits_{0}^{3/2}[x^{2}]dx[/tex]=?

[Knowledge Greedy]

Разбиваме интеграла на три:
[tex]\int \limits_{0}^{1}0dx=0[/tex]

[tex]\int \limits_{1}^{\sqrt{2}}1dx=x\left|\begin{matrix}
\sqrt2\\
\\
1
\end{matrix}\right.=\sqrt2-1[/tex]

[tex]\int\limits_{\sqrt2}^{\frac{9}{4}}2dx=2x\left|\begin{matrix}
\frac{3}{2}\\
\\
\sqrt2
\end{matrix}\right.=3-2\sqrt2[/tex]

Отговор: [tex]2-\sqrt{2}[/tex]