The area bounded by the lines y = x,x = -1,x | vedclass

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Question

(A) The area is given by the integral of the absolute value of $y$ with respect to $x$ from $x = -1$ to $x = 2$.Area $= \int_{-1}^{2} |y| \, dx = \int

Vedclass · Accepted Answer

$\frac{5}{2} 	ext{ sq. unit}$

Vedclass · Answer

(A) The area is given by the integral of the absolute value of $y$ with respect to $x$ from $x = -1$ to $x = 2$.Area $= \int_{-1}^{2} |y| \, dx = \int_{-1}^{2} |x| \, dx$Since $|x| = -x$ for $x Area $= \int_{-1}^{0} (-x) \, dx + \int_{0}^{2} (x) \, dx$$= \left[ -\frac{x^2}{2} ight]_{-1}^{0} + \left[ \frac{x^2}{2} ight]_{0}^{2}$$= (0 - (-\frac{(-1)^2}{2})) + (\frac{2^2}{2} - 0)$$= \frac{1}{2} + 2 = \frac{5}{2} 	ext{ sq. unit}$.

The area bounded by the lines $y = x$,$x = -1$,$x = 2$ and the $x$-axis is

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