Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by Miscellaneous CurvesMedium2 minQB

MathematicsMediumsingle choice

The largest area of the rectangle which has one side on the X -axis and two vertices on the curve $y = e^{- x^{2}}$ is

Answer:

Solution:

Let $f (t) = t e^{- t^{2}}$

$f^{1} (t) = - 2 t^{2} e^{- t^{2}} + e^{- t^{2}}$

$= e^{- t^{2}} (1 - 2 t^{2})$

$f^{1} (t) = 0 \Rightarrow t = \frac{1}{2}$

Max area $= 2 \times \frac{1}{2} \times e^{\frac{- 1}{2}} = \frac{2}{e}$

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

⏱ 2mℹ️ Source: QB

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