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Evaluate int(pi/6)^(pi/3)(dx)/(1+sqrt(t...

Evaluate `int_(pi/6)^(pi/3)(dx)/(1+sqrt(tanx))`

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To evaluate the integral \[ I = \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{dx}{1 + \sqrt{\tan x}}, \] we can use a substitution to simplify the integral. ...
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Knowledge Check

  • Statement I: The value of the integral int_(pi//6)^(pi//3) (dx)/(1+sqrt(tanx)) is equal to (pi)/6 . Statement II: int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx

    A
    Statement I is true, statement II is true, statement II is a correct explanation for statement I
    B
    Statement I is true, statement II is true, statement II is a not a correct explanation for statement I
    C
    Statement I is true, statement II is false
    D
    Statement I is false, statement II is true

  • I_(1) = int_(pi/6)^(pi/3) (dx)/(1+sqrt(tanx)) and I_(2) = (sqrt(sinx)dx)/(sqrt(sinx) + sqrt(cosx)) What is I_(1) equal to ?

    A
    `pi//24`
    B
    `pi//18`
    C
    `pi//12`
    D
    `pi//6`

  • I_(1) = int_(pi/6)^(pi/3) (dx)/(1+sqrt(tanx)) and I_(2) = (sqrt(sinx)dx)/(sqrt(sinx) + sqrt(cosx)) What is I_(1) - I_(2) equal to ?

    A
    0
    B
    `2I_(1)`
    C
    `pi`
    D
    None of the above

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