Question

11.Given that

$∫\frac{dx}{ \sqrt{2ax + x {}^{2} } } = a {}^{n} sin { }^{ - 1} ( \frac{x - a}{a} )$
Where a = constant. Using dimensional analysis, the value of n is:
a. 1
b. 0
C. -1
d. none of these​

Answer 1

Answer:

0

Dimension of a has to be the same as that of x for x−a to be a valid expression in the right side. Hence,

2ax−x

2

has the dimensions of x , which implies the dimensions of the numerator and denominator are same on the left hand side. For the term to be dimensionless on the right hand side too, n must be equal to zero.