Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesVariable Area ( greatest and Least ValuesHard2 minQB

MathematicsHardsingle choice

Passage / Comprehension

Let $f (x) = x ln x$ . For $0 < a < 1$ , let $Δ$ be the area bounded by $y = f (x), x = a, x = a^{3}$ , and the $x$ -axis.

Find the maximum value of $Δ$ .

Answer:

Solution:

Using $\int x ln x d x = \frac{x ^{2}}{2} ln x - \frac{x ^{2}}{4}$ and substituting $a = 1/ 3$ gives $Δ_{m a x} = (4 + ln 27) /54$ .

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Variable Area ( greatest and Least Values

⏱ 2mℹ️ Source: QB

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