Question

Tính \(\int\limits^2_1\left(x^3-x\right)dx\).

Answer 1

\(\int\limits_1^2 {({x^3} - x)dx} = \int\limits_1^2 {{x^3}dx} - \int\limits_1^2 {xdx} = \frac{{{x^4}}}{4}\left| {\begin{array}{*{20}{c}}{^2}\\{_1}\end{array}} \right. - \frac{{{x^2}}}{2}\left| {\begin{array}{*{20}{c}}{^2}\\{_1}\end{array}} \right.\)

\( = \frac{{{2^4}}}{4} - \frac{{{1^4}}}{4} - \left( {\frac{{{2^2}}}{2} - \frac{{{1^2}}}{2}} \right) = \frac{9}{4}\).