Question

In the integral `int("d"x)/((2"a"x-x^2)^(1/2)) = "a"^"n" sin^-1 (x/"a"-1)`, the value of n should be ______.

Options

• 1

• -1

• 0

• `1/2`

Answer 1

In the integral `int("d"x)/((2"a"x-x^2)^(1/2)) = "a"^"n" sin^-1 (x/"a"-1)`, the value of n should be 0.

Explanation:

`int("d"x)/((2"a"x-x^2)^(1/2)) = "a"^"n" sin^-1 (x/"a"-1)`

From R.H.S. dimension of [a] = [L],

Since `[x/"a"]` should be dimensionless,

Dimension L.H.S.: `["L"]/["L"]` = L° 

Since dimension of [2ax – x²]^1/2 = [L]

and dimension of [dx] = L

Equating dimensions of L.H.S. and R.H.S.

L° = Lⁿ

n = 0