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| If \([x]\) denotes the greatest integer function of \(x\) then \(\int_{a}^{b}[x]dx+\int_{b}^{a}[-x]dx=\) |
\(2(b-a)\) \(2(a-b)\) \(a-b\) \(0\) |
| \(2(b-a)\) |
| \(\begin{aligned}\int_{a}^{b}[x]dx+\int_{b}^{a}[-x]dx&=[x]_{a}^{b}+[-x]_{b}^{a}\\ &=2(b-a)\end{aligned}\) |
