[latex] \int\limits^a_b {(4-x^2)x} \, dx [/latex]

[latex]\int (4-x^2)\cdot xdx=[t=4-x^2,dt=-2xdx,xdx=-\frac{dt}{2}]=\\\\=-\frac{1}{2}\cdot \int t\cdot dt=-\frac{1}{2}\cdot \frac{t^2}{2}+C=-\frac{t^2}{4}+C=-\frac{(4-x^2)^2}{4}+C\\\\\\\int _{a}^{b}(4-x^2)\cdot xdx=-\frac{(4-x^2)^2}{4}|_{a}^{b}=-\frac{1}{4}((4-b^2)^2-(4-a^2)^2)=\\\\=-\frac{1}{4}(b^4-a^4-8b^2+8a^2)[/latex]