Find the area satisfying ∣ x − y ∣ + ∣ x + y ∣ 2 , x > 0 , y > 0 .

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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by Miscellaneous CurvesMedium2 minQB

MathematicsMediumsingle choice

Find the area satisfying $∣ x - y ∣ + ∣ x + y ∣ < 8, x y > 2, x > 0, y > 0$ .

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Answer:

Solution:

In the first quadrant the absolute-value inequality gives the square $0 < x, y < 4$ . Removing the part below $y = 2/ x$ gives $14 - \int_{1/2}^{4} (2/ x) d x = 14 - ln 64$ .

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area bounded by Miscellaneous Curves

⏱ 2mℹ️ Source: QB

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