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Let int(0)^(1) (dx )/( sqrt(16 + 9x ^(2)...

Let `int_(0)^(1) (dx )/( sqrt(16 + 9x ^(2)))+ int _(0) ^(2) (dx)/(sqrt (9+4x ^(2)))= lna. `Find a.

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Verified by Experts

The correct Answer is:
`2 ^(1//3). 3 ^(1//2)`
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Knowledge Check

  • int(dx)/(sqrt(4-9x^(2)))=?

    A
    `(1)/(3) sin^(-1)""(x)/(3)+C`
    B
    `(2)/(3) sin^(-1)""((2x)/(3))+C`
    C
    `(1)/(3) sin^(-1)""((3x)/(2))+C`
    D
    None of these

  • int(dx)/(sqrt(9-25x^(2)))

    A
    `sin^(-1)((5x)/(3))+c`
    B
    `(1)/(5)sin^(-1)((5x)/(3))+c`
    C
    `(1)/(6)log ((3+5x)/(3-5x))+c`
    D
    `(1)/(30)log ((3+5x)/(3-5x))+c`

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    int(dx)/(sqrt(9x^(2)-4))

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