First slide

Integration

Question

$\int \frac{dt}{\sqrt{2 at - t^{2}}} = a^{x} \sin^{- 1} [\frac{t}{a} - 1]$ The value of x is

Difficult

A

1
B

-1
C

0
D

2

Solution

The quantity $\frac{t}{a} - 1 is dimensionless i . e; [a] = [t]$
$∴ [\sqrt{2 at - t^{2}}] = [t]$
or $[\frac{dt}{\sqrt{2 at - t^{2}}}] = [\frac{t}{t}] = [M^{0} L^{0} T^{0}]$
i.e $a^{x} should also be dimensionless or x = 0$

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