Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesHard2 minPYQ_2023

MathematicsHardsingle choice

The area enclosed between the curves $y^{2} + 4 x = 4$ and $y - 2 x = 2$ is

Answer:

Solution:

Given:

$y^{2} = - 4 x + 4$

$y = 2 x + 2$

Required area

$= \int_{- 4}^{2} (\frac{4 - y^{2}}{4} - \frac{y - 2}{2}) d y$

$= \int_{- 4}^{2} (2 - \frac{y^{2}}{4} - \frac{y}{2}) d y$

$= {[2 y - \frac{y^{3}}{12} - \frac{y^{2}}{4}]}_{- 4}^{2}$

$= [(4 - \frac{8}{12} - 1) - (- 8 + \frac{64}{12} - \frac{16}{4})]$

$= 15 - 6$

$= 9$ sq. units

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

⏱ 2mℹ️ Source: PYQ_2023

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