Area enclosed by the curve y = f ( x ) defined parametrically as x = 1 + t 2 1 − t 2 , y = 1 + t 2 2 t is equal to

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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by Miscellaneous CurvesMedium2 minQB

MathematicsMediumsingle choice

Area enclosed by the curve $y = f (x)$ defined parametrically as $x = \frac{1 - t ^{2}}{1 + t ^{2}}, y = \frac{2 t}{1 + t ^{2}}$ is equal to

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Solution:

Putting $t = tan θ : x = cos 2 θ, y = sin 2 θ$ , so $x^{2} + y^{2} = 1$ . As $t$ ranges over all real numbers the full unit circle is traced, whose area is $π$ .

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

⏱ 2mℹ️ Source: QB

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