步骤 3:分段计算

第 1 部分(为负,取绝对值):

\(\left| \int_{-2}^{2} (x^2-4) \, dx \right| = \left| \Big[ \frac{x^3}{3} - 4x \Big]_{-2}^{2} \right|\)

\(= \left| \left(\frac{8}{3} - 8\right) - \left(\frac{-8}{3} + 8\right) \right|\)

\(= \left| -\frac{16}{3} - \frac{16}{3} \right| = \left| -\frac{32}{3} \right| = \frac{32}{3}\)

第 2 部分(为正):

\(\int_{2}^{3} (x^2-4) \, dx = \Big[ \frac{x^3}{3} - 4x \Big]_{2}^{3}\)

\(= \left(9 - 12\right) - \left(\frac{8}{3} - 8\right)\)

\(= -3 + \frac{16}{3} = \frac{7}{3}\)