First slide

Integration

Question

If equation $\int \frac{dt}{\sqrt{3 at - 2 t^{2}}} = a^{x} \sin^{- 1} (\frac{t^{2}}{a^{2}} - 1)$ , the value of x is

Moderate

A

$\frac{3}{2}$
B

0
C

$\frac{1}{2}$
D

- $\frac{1}{2}$

Solution

$(\frac{t^{2}}{a^{2}} - 1)$ is dimensionless
$∴$ [a] = [t]
As, $\sqrt{(3 at - 2 t^{2})} = [t]$
$∴ [\frac{dt}{\sqrt{3 at - t^{2}}}] = \frac{[t]}{[t]} = [M^{0} L^{0} T^{0}]$
$a^{x}$ should be dimensionless, so x = 0.

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