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\(\int_{0}^{3}[x]dx=\) (where \([\cdot]\) denotes the greatest integer function). |
2 3 1 0 |
3 |
\(\int_{0}^{3}[x]dx=\int_{0}^{1}[dx]dx+\int_{1}^{2}[x]dx+\int_{2}^{3}[x]dx\) $=\int_{0}^{1}0dx+\int_{1}^{2}1dx+\int_{2}^{3}2dx$ $=1×(2-1)+2×(3-2)$ $=3$ |
