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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by Miscellaneous CurvesHard2 minQB

MathematicsHardsingle choice

Continuous increasing odd $f$ satisfies $f^{- 1} (4) = f (4) = α$ . The area under $f^{- 1}$ from 0 to $α$ is 10 . Find the area under $f$ from 0 to $α$ .

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Answer:

Solution:

Monotonicity and $f^{- 1} (4) = f (4) = α$ force $α = 4$ . The inverse-area identity gives $\int_{0}^{4} f + \int_{0}^{4} f^{- 1} = 16$ , so the required area is $16 - 10 = 6$ .

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

⏱ 2mℹ️ Source: QB

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