The area bounded by the line $y - x$ , x-axis and lines $x = -1$ to $x = 2$, is
Updated On: Jul 7, 2022
$0$ s unit
$1/2$ s unit
$3/2$ s unit
$5/2$ s unit
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The Correct Option isD
Solution and Explanation
We have $y=x$
Required area = area of shaded region
$A=\left|\int\limits_{-1}^{0}x dx\right|+\left|\int\limits_{0}^{2}xdx\right|=\left|\frac{x^{2}}{2}\right|_{-1}^{0}+\left|\frac{x^{2}}{2}\right|_{0}^{2}$$=\left|-\frac{1}{2}\right|+\left|2\right|=2+\frac{1}{2}=\frac{5}{2}$ s units
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Concepts Used:
Area under Simple Curves
The area of the region bounded by the curve y = f (x), x-axis and the lines x = a and x = b (b > a) - given by the formula:
\[\text{Area}=\int_a^bydx=\int_a^bf(x)dx\]
The area of the region bounded by the curve x = φ (y), y-axis and the lines y = c, y = d - given by the formula:
