Evaluate the following integrals: ^2_0 [x ]dx - Vidyadip

Question

Evaluate the following integrals:
$\int\limits^2_0\big[\text{x}\big]\text{dx}$

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Answer

we have,
$\text{I}=\int\limits^2_0\big[\text{x}\big]\text{dx}$
$=\int\limits^1_0\big[\text{x}\big]\text{dx}+\int\limits^2_1\big[\text{x}\big]\text{dx}$
$=\int\limits^1_00\text{ dx}+\int\limits^2_1(\text{1})\text{dx}$ $\begin{bmatrix}\because\big[\text{x}\big]=\begin{cases}0,&0\leq\text{x}<1\\1,&1\leq\text{x}<2\end{cases}\end{bmatrix}$
$=0+\big[\text{x}\big]^{2}_1$
$=2-1$
$=1$

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