Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by Miscellaneous CurvesMedium2 minPYQ_2019

MathematicsMediumsingle choice

Area bounded by two branches of the curve ${(y - x)}^{2} = x^{3}$ and $x = 1$ is

Answer:

Solution:

Given, curve is ${(y - x)}^{2} = x^{3}$

$\Rightarrow y - x = \pm x \sqrt{x}$

$\Rightarrow y = x \pm x \sqrt{x}$

$∴$ Area bounded $= |\int_{0}^{1} \{(x + x \sqrt{x}) - (x - x \sqrt{x})\} d x|$

$= |2 \int_{0}^{1} x^{3 / 2} d x| = \frac{4}{5} sq unit$

Stream:BITSATSubject:MathematicsTopic:Area Under CurvesSubtopic:Area bounded by Miscellaneous Curves

⏱ 2mℹ️ Source: PYQ_2019

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