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Area bounded by the lines $y=x, x=-1, x=2$ and $x$ -axis is
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The correct answer is:
$5 / 2$ sq unit
Required area $=\int_{-1}^{2} y d x$
$=\int_{-1}^{0} y d x+\int_{0}^{2} y d x$
$=\left|\int_{-1}^{0} x d x\right|+\int_{0}^{2} x d x$
$\left.=\mid \frac{x^{2}}{2}\right]_{1}^{0} \mid+\left[\frac{x^{2}}{2}\right]_{0}^{2}=\frac{5}{2}$ sq unit
$=\int_{-1}^{0} y d x+\int_{0}^{2} y d x$
$=\left|\int_{-1}^{0} x d x\right|+\int_{0}^{2} x d x$
$\left.=\mid \frac{x^{2}}{2}\right]_{1}^{0} \mid+\left[\frac{x^{2}}{2}\right]_{0}^{2}=\frac{5}{2}$ sq unit
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