The area enclosed by the curves y = x 3 and y = x is

Since, the intersection of two curves y = x 3 and y = x are x = 0 and x = 1 ∴ A = ∫ 0 1 x 3 - x d x = x 4 4 - 2 x 3 / 2 3 0 1 = 1 4 - 2 3 = 5 12 sq units

Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesMedium2 minPYQ_2017

MathematicsMediumsingle choice

The area enclosed by the curves $y = x^{3}$ and $y = \sqrt{x}$ is

Options:

Answer:

Solution:

Since, the intersection of two curves

$y = x^{3}$ and $y = \sqrt{x}$ are $x = 0$ and $x = 1$

$∴ A = |\int_{0}^{1} (x^{3} - \sqrt{x}) d x| = |{[\frac{x^{4}}{4} - \frac{2 x^{3 / 2}}{3}]}_{0}^{1}|$

$= |[\frac{1}{4} - \frac{2}{3}]| = \frac{5}{12} sq units$

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

⏱ 2mℹ️ Source: PYQ_2017

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