area bounded by the curves y=lxl and y=4=lxl is

a)4 b)16 c)2 d)8

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area bounded by the curves y=lxl and y=4=lxl is
a)4 b)16 c)2 d)8

Lalit Mehra · Accepted Answer

The given curves are $y = | x | and y = 4 – | x |$ $| x | = {\begin{matrix} x, x \geq 0 \\ - x, x < 0 \end{matrix}$ When x â‰¥ 0, $y = | x | = x$ and $y = 4 - | x | = 4 - x$ When x < 0, $y = | x | = - x$ and $y = 4 - | x | = 4 - (- x) = 4 + x$ The graph of the given curves is shown as,

Area bounded by the curve = Area of the shaded region $= \int_{- 2}^{0} [(4 + x) - (- x)] d x + \int_{0}^{2} [(4 - x) - x] d x = \int_{- 2}^{0} (4 + 2 x) d x + \int_{0}^{2} (4 - 2 x) d x = \frac{(4 + 2 x)^{2}}{2 \times 2} |_{- 2}^{0} + \frac{(4 - 2 x)^{2}}{2 \times (- 2)} |_{0}^{2} = \frac{1}{4} [(4 + 2 \times 0)^{2} - (4 + 2 \times (- 2))^{2}] - \frac{1}{4} [(4 - 2 \times 2)^{2} - (4 - 2 \times 0)^{2}] = \frac{1}{4} (16 - 0) - \frac{1}{4} (0 - 16) = \frac{1}{4} \times 16 + \frac{1}{4} \times 16 = 4 + 4 = 8$ Thus, the area bounded by the curves is 8 sq units

area bounded by the curves y=lxl and y=4=lxl is a)4 b)16 c)2 d)8

area bounded by the curves y=lxl and y=4=lxl is

a)4 b)16 c)2 d)8