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Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by Miscellaneous CurvesHard2 minPYQ_2009

MathematicsHardmultiple choice

Area of the region bounded by the curve $y = e^{x}$ and lines $x = 0$ and $y = e$ is

Question diagram: Area of the region bounded by the curve y = e x and lines x

Options:(select one or more)

Answer:

B, C, D

Solution:

Shaded area $= e - (\int_{0}^{1} e^{x} d x) = 1$ Also, $\int_{1}^{e} ln (e + 1 - y) d y$
$= \int_{e}^{q} ln t (- d t) [put e + 1 - y = t \Rightarrow - d y = d t] = \int_{1}^{e} ln t d t = \int_{1}^{e} ln y d y = 1$

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

⏱ 2mℹ️ Source: PYQ_2009

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