[latex] intlimits^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 tcdot 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]