Value of ∫ x ( a − x ) d x is

Let x = a sin 2 θ then d x = 2 a sin θ cos θ d θ ∴ I = ∫ a sin 2 θ ⋅ a cos 2 θ 2 a sin θ ⋅ cos θ d θ = 2 ∫ d θ = 2 θ + c = 2 sin − 1 ( x / a ) + c

Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationSubstitutionMedium2 minPYQ_2023

MathematicsMediumsingle choice

Value of $\int \frac{d x}{x ( a - x )}$ is

Options:

Answer:

Solution:

Let $x = a sin^{2} θ$
then $d x = 2 a sin θ cos θ d θ$
$∴ I = \int \frac{2 a sin θ \cdot cos θ}{a sin ^{2} θ \cdot a cos ^{2} θ} d θ = 2 \int d θ = 2 θ + c = 2 sin^{- 1} (x / a) + c$

Stream:BITSATSubject:MathematicsTopic:Indefinite IntegrationSubtopic:Substitution

⏱ 2mℹ️ Source: PYQ_2023

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