Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesMedium2 minPYQ_2008

MathematicsMediumsingle choice

The area of the plane region bounded by the curves $x + 2 y^{2} = 0$ and $x + 3 y^{2} = 1$ is equal to

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Answer:

Solution:

Solving the equations we get the points of intersection $(- 2, 1)$ and $(- 2, - 1)$ The bounded region is shown as shaded region. $The required area = 2 \int_{0}^{1} (1 - 3 y^{2}) - (- 2 y^{2}) = 2 \int_{0}^{1} (1 - y^{2}) d y = 2 [y - \frac{y ^{3}}{3}]_{0}^{1} = 2 \times \frac{2}{3} = \frac{4}{3} .$

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

⏱ 2mℹ️ Source: PYQ_2008

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