If the area of the region bounded by the curves, y = x 2 , y = 1 x and the lines y = 0 and x = t t > 1 is 1 sq . unit , then t is equal to

Area = ∫ 0 1 x 2 d x + ∫ 1 t 1 x d x = 1 ⇒ 1 3 + ln t = 1 ⇒ t = e 2 3

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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesMedium2 minPYQ_2018

MathematicsMediumsingle choice

If the area of the region bounded by the curves, $y = x^{2}, y = \frac{1}{x}$ and the lines $y = 0$ and $x = t (t > 1)$ is $1 sq . unit$ , then $t$ is equal to

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Answer:

Solution:

Area $= \int_{0}^{1} x^{2} d x + \int_{1}^{t} \frac{1}{x} d x = 1$

$\Rightarrow \frac{1}{3} + \ln (t) = 1 \Rightarrow t = e^{\frac{2}{3}}$

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area bounded by two curves

⏱ 2mℹ️ Source: PYQ_2018

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