Question

If `int(x + (cos^-1 3x)^2)/sqrt(1 - 9x^2)dx = 1/α(sqrt(1 - 9x^2) + (cos^-1 3x)^β) + C`, where C is constant of integration , then (α + 3β) is equal to ______.

विकल्प

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

If `int(x + (cos^-1 3x)^2)/sqrt(1 - 9x^2)dx = 1/α(sqrt(1 - 9x^2) + (cos^-1 3x)^β) + C`, where C is constant of integration , then (α + 3β) is equal to 0.00.

Explanation:

`int(x + (cos^-1 3x)^2)/sqrt(1 - 9x^2)dx = (-1)/9(sqrt(1 - 9x^2) + (cos^-1 3x)^3) + C`

∴ α = – 9, β = 3

⇒ (α + 3β) = 0