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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea of Curve along axisEasy2 minPYQ_2022

MathematicsEasysingle choice

The odd natural number a, such that the area of the region bounded by $y = 1, y = 3, x = 0, x = y^{a}$ is $\frac{364}{3}$ , equal to:

Question diagram: The odd natural number a, such that the area of the region b

Options:

Answer:

B

Solution:

Plotting the graph of the given functions, we get the shaded region as the area bounded by the curves.
Given, area of shaded region $= \frac{364}{3}$
$\Rightarrow \int_{1}^{3} y^{a} d y = \frac{364}{3}$
$\Rightarrow {[\frac{y^{a + 1}}{a + 1}]}_{1}^{3} = \frac{364}{3}$
$\Rightarrow \frac{3^{a + 1} - 1}{a + 1} = \frac{364}{3} = \frac{729 - 1}{6} = \frac{3^{6} - 1}{6}$
$\Rightarrow a = 5$

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

⏱ 2mℹ️ Source: PYQ_2022

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