The area of the region enclosed by the lines | vedclass

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Question

(C) The lines are $y = 2x$, $y = x/2$, and $x = 2$.The intersection of $y = 2x$ and $y = x/2$ is at $(0, 0)$.The intersection of $y = 2x$ and $x = 2$

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) The lines are $y = 2x$, $y = x/2$, and $x = 2$.The intersection of $y = 2x$ and $y = x/2$ is at $(0, 0)$.The intersection of $y = 2x$ and $x = 2$ is at $(2, 4)$.The intersection of $y = x/2$ and $x = 2$ is at $(2, 1)$.The area $A$ is given by the integral $\int_{0}^{2} (2x - x/2) \, dx$.$A = \int_{0}^{2} (3x/2) \, dx$.$A = \frac{3}{2} \left[ \frac{x^2}{2} ight]_{0}^{2}$.$A = \frac{3}{4} [4 - 0] = 3 	ext{ sq. units}$.

The area of the region enclosed by the lines $y = 2x$, $2y = x$ and $x = 2$ (in sq. units) is...

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