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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.

When is $Δ$ extremal?

Options:

Answer:

Solution:

$Δ (a) = \int_{a}^{a^{3}} x ln x d x$ with orientation chosen for positive area. Leibniz differentiation gives $Δ t = a ln a (9 a^{4} - 1)$ , whose sign changes from positive to negative at $a = 1/ 3$ .

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

⏱ 2mℹ️ Source: QB

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