Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea of Curve along axisMedium2 minPYQ_2019

MathematicsMediumsingle choice

Let $S (α) = \{(x, y) : y^{2} \leq x, 0 \leq x \leq α\}$ and $A (α)$ is area of the region $S (α) .$ If for a $λ, 0 < λ < 4, A (λ) : A (4) = 2 : 5,$ then $λ$ equals:

Options:

Answer:

Solution:

$S (λ) = 2 \int_{0}^{λ} \sqrt{x} d x = 2 {[\frac{x^{\frac{3}{2}}}{\frac{3}{2}}]}_{0}^{λ}$
$= \frac{4}{3} λ^{\frac{3}{2}}$
$∴ S (4) = \frac{4}{3} {(4)}^{\frac{3}{2}}$
Given $\frac{S (λ)}{S (4)} = \frac{2}{5} \Rightarrow \frac{λ^{\frac{3}{2}}}{4^{\frac{3}{2}}} = \frac{2}{5}$
$\Rightarrow λ = 4 {(\frac{4}{25})}^{\frac{1}{3}}$

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area of Curve along axis

⏱ 2mℹ️ Source: PYQ_2019

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