Evaluate: ∫ 4 − x 3 x dx

I = ∫ 4 − x 3 x d x = ∫ 4 − x 3 x d x Here integral of x = 3 2 x 3/2 and 4 − x 3 = 4 − ( x 3/2 ) 2 Put x 3/2 = t ⇒ x d x = 3 2 d t So I = 3 2 ∫ 4 − t 2 d t = 3 2 sin − 1 ( 2 x 3/2 ) + c

Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationSubstitutionMedium2 minPYQ_2012

MathematicsMediumsingle choice

Evaluate: $\int \frac{x}{4 - x ^{3}} dx$

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Solution:

$I = \int \frac{x}{4 - x ^{3}} d x = \int \frac{x d x}{4 - x ^{3}}$ Here integral of $x = \frac{2}{3} x^{3/2}$ and $4 - x^{3} = 4 - (x^{3/2})^{2}$ Put $x^{3/2} = t \Rightarrow x d x = \frac{2}{3} d t$ So $I = \frac{2}{3} \int \frac{d t}{4 - t ^{2}} = \frac{2}{3} sin^{- 1} (\frac{x ^{3/2}}{2}) + c$

Stream:BITSATSubject:MathematicsTopic:Indefinite IntegrationSubtopic:Substitution

⏱ 2mℹ️ Source: PYQ_2012

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