Evaluate the following integrals: ^ 1.5 _0 [x ]dx - Vidyadip

Question

Evaluate the following integrals:$\int\limits^{1.5}_0\big[\text{x}\big]\text{dx}$

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Answer

We have,$\text{I}=\int\limits^{1.5}_0\big[\text{x}\big]\text{dx}$
$=\int\limits^{1}_0\big[\text{x}\big]\text{dx}+\int\limits^{1.5}_0\big[\text{x}\big]\text{dx}$
$=\int\limits^{1}_0(0)\text{dx}+\int\limits^{1.5}_0(1)\text{dx}$ $\begin{bmatrix}\because\big[\text{x}\big]=\begin{cases}0,&0\leq\text{x}<1\\1,&1\leq\text{x}<1.5\end{cases}\end{bmatrix}$
$=0+\big[\text{x}\big]^{1.5}_1$
$=1.5-1$
$=\frac{1}{2}$

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