Find thrice the area of the region bounded by the curve $y^{2} = 2 y - x$ and the y-axis.

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Solution

$A = (0, 0)$ , $B = (0, 2)$
Area of shaded region
$= - \int_{0}^{2} y^{2} - 2 y d y$
$= [\frac{y^{3}}{3}]_{2}^{0} - [y^{2}]_{2}^{0}$
$= 4 - \frac{8}{3}$
$A = \frac{4}{3}$
$3 A = 4$

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Similar questions

Area of the region bounded by the curve y² = 2y - x and y-axis is:

x^{2} = 16 y, y = 1, y = 4

y

y = \sqrt{4 - x^{2}}, x^{2} + y^{2} - 4 x = 0

y^{2} = 2 y - x

y

x = 4 y - y^{2}

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