Area bounded by the curve x = ⎩ ⎨ ⎧ − 2 − y y 3 2 − y ; y 1 and x = 0 is -

required area = 2 ∫ 0 1 [ ( 2 − x ) − x 1/3 ] dx = 2 [ 2 x − 2 x 2 − 4 3 x 4/3 ] 0 1 = 2 ( 2 − 2 1 − 4 3 ) = 2 3 .

Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea of Curve along axisMedium2 minQB

MathematicsMediumsingle choice

Area bounded by the curve $x = ⎩ ⎨ ⎧ - 2 - y y^{3} 2 - y; y < - 1; - 1 \leq y \leq 1; y > 1$ and $x = 0$ is -

Answer:

Solution:

required area $= 2 \int_{0}^{1} [(2 - x) - x^{1/3}] dx$

$= 2 [2 x - \frac{x ^{2}}{2} - \frac{3 x ^{4/3}}{4}]_{0}^{1} = 2 (2 - \frac{1}{2} - \frac{3}{4}) = \frac{3}{2} .$

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

⏱ 2mℹ️ Source: QB

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