Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesEasy2 minPYQ_2022

MathematicsEasynumerical

The area (in sq. units) of the region enclosed between the parabola $y^{2} = 2 x$ and the line $x + y = 4$ is ______.

Answer:

18.00

Solution:

$y^{2} = 2 x \Rightarrow y^{2} = 2 (4 - y)$

$\Rightarrow y^{2} + 2 y - 8 = 0 \Rightarrow y = - 4, 2$

The point of intersection of $y^{2} = 2 x$ and $x + y = 4$ are $(8, - 4)$ and $(2, 2)$

Area $= \int_{- 4}^{2} ((4 - y) - \frac{y^{2}}{2}) d y = {(4 y - \frac{y^{2}}{2} - \frac{y^{3}}{6})}_{- 4}^{2}$

$= (8 - 2 - \frac{4}{3}) - (- 16 - 8 + \frac{32}{3})$

$= \frac{54}{3} = 18$ Sq.units.

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area bounded by two curves

⏱ 2mℹ️ Source: PYQ_2022

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