The area (in sq. units) of the region described by $\left\{(x, y): y^2 \leq 2 x\right.$, and $\left.y \geq 4 x-1\right\}$ is

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Aicharya · Accepted Answer

$\begin{aligned} & 	ext { Shaded area }=\int_{-\frac{1}{2}}^1\left(x_{	ext {Right }}-x_{	ext {Left }}ight) d y \ & y^2=2 x \ & y=4 x-1 \quad 	ext { Solve } \ & y=1, y=-\frac{1}{2} \ & 	ext { Shaded area }=\int_{-\frac{1}{2}}^1\left(\frac{y+1}{4}-\frac{y^2}{2}ight) d y \ & =\left(\frac{1}{4}\left(\frac{y^2}{2}+yight)-\frac{y^3}{6}ight)_{-\frac{1}{2}}^1=\frac{9}{32}\end{aligned}$

The area (in sq. units) of the region described by $\left\{(x, y): y^2 \leq 2 x\right.$, and $\left.y \geq 4…

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