If αβ∫x+(cos-13x)21-9x2dx=1α(1-9x2+(cos-13x)β)+C, where C is constant of integration , then (α + 3β) is equal to ______. - Mathematics (JEE Main)

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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 ______.

Options

  • 0.00

  • 1.00

  • 2.00

  • 3.00

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Solution

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

  Is there an error in this question or solution?

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