In the equation ∫ 2 a x − x 2 d x = a n sin − 1 ( a x − 1 ) . Find the value of n .

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Physics - Unit & Dimension Question with Solution | TestHub

PhysicsUnit & DimensionMiscellaneousMedium2 minQB

PhysicsMediuminteger

In the equation $\int \frac{d x}{2 a x - x ^{2}} = a^{n} sin^{- 1} (\frac{x}{a} - 1)$ . Find the value of $n$ .

Answer:

Solution:

$\frac{d x}{2 a x - x ^{2}}$
is dimensionless.Therefore
$a^{n} sin^{- 1} (\frac{x}{a} - 1)$
should also be dimensionless.
Since the sine term is dimensionless, $a^{n}$ must be dimensionless.
Hence, $n = 0$ .

Stream:JEESubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

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