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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 ______.
Options
0.00
1.00
2.00
3.00
MCQ
Fill in the Blanks
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
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