The area bounded by the lines y=x,x=-1,x=2 an | vedclass

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Question

(C) The required area is the sum of the absolute values of the integrals over the intervals where the function is negative and positive.$A = \int_{-1}

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$\frac{5}{2}$ sq. units

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(C) The required area is the sum of the absolute values of the integrals over the intervals where the function is negative and positive.$A = \int_{-1}^{0} |x| dx + \int_{0}^{2} |x| dx$Since $x  0$ for $x \in [0, 2]$,we have:$A = \int_{-1}^{0} (-x) dx + \int_{0}^{2} (x) dx$$A = \left[ -\frac{x^2}{2} ight]_{-1}^{0} + \left[ \frac{x^2}{2} ight]_{0}^{2}$$A = (0 - (-\frac{(-1)^2}{2})) + (\frac{2^2}{2} - 0)$$A = \frac{1}{2} + 2 = \frac{5}{2} 	ext{ sq. units}$

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

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