The area of the region enclosed by y ≤ 4 x 2 , x 2 ≤ 9 y and y ≤ 4 , is equal to

Plotting the required region Enclosed area = 2 ∫ 0 4 3 y - y 2 d y = 2 ∫ 0 4 5 y 2 d y = 5 2 3 y 3 2 0 4 = 10 3 ( 4 ) 3 2 = 80 3

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MathematicsArea Under CurvesArea bounded by two curvesEasy2 minPYQ_2022

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The area of the region enclosed by $y \leq 4 x^{2}, x^{2} \leq 9 y$ and $y \leq 4$ , is equal to

Question diagram: The area of the region enclosed by y ≤ 4 x 2 , x 2 ≤ 9 y and

Options:

Answer:

Solution:

Plotting the required region
Enclosed area $= 2 \int_{0}^{4} (3 \sqrt{y} - \frac{\sqrt{y}}{2}) d y$
$= 2 \int_{0}^{4} \frac{5 \sqrt{y}}{2} d y$
$= 5 {[\frac{2}{3} y^{\frac{3}{2}}]}_{0}^{4}$
$= \frac{10}{3} (4)^{\frac{3}{2}} = \frac{80}{3}$

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

⏱ 2mℹ️ Source: PYQ_2022

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