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Question
Solution
\[\text{We have}, \]
\[I = \int_0^2 \left[ x \right] d x\]
\[\text{We know that}, \]
\[\left[ x \right] = \begin{cases}0&,& 0 < x < 1\\1&,& 1 < x < 2\end{cases}\]
\[ \therefore I = \int_0^2 \left[ x \right] d x\]
\[ = \int_0^1 \left[ x \right] d x + \int_1^2 \left[ x \right] d x\]
\[ = \int_0^1 \left( 0 \right) d x + \int_1^2 \left( 1 \right) d x\]
\[ = 0 + \left[ x \right]_1^2 \]
\[ = 2 - 1 = 1\]
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