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Let $[t]$ denote the greatest integer less than or equal to $t$. Then the value of $\int_1^2 |2x - [3x]|,dx$ is ______.
$\int_1^2 |3x - x - [3x]|,dx = \int_1^2 |{3x} - x|,dx$. Evaluating piecewise: $= \int_1^{1/3} x,dx - \int_1^{1/3} {3x},dx = \frac{3}{2} - \frac{1}{2} = 1$.
BETA
