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Thread: Evaluate the Integral

  1. #1

    Evaluate the Integral

    Is this the correct answer?


    Evaluate the following integrals


    1
    ∫ ((2x)/(sqrt1+2x))dx
    0


    ITG = (2/3)*(x-1)*sqrt(2x+1) + C

    ITG(1) = 0
    ITG(0) = -2/3
    ITG(1) - ITG(0) = 2/3
    --> 2/3

  2. #2
    Senior Member
    Join Date
    Jan 2012
    Posts
    2,339
    No, it isn't. Unfortunately, since you did not show how you did the integral, I cannot say how to correct it. Did you make the sustitution u= 1+ 2x?

  3. #3
    I attached a picture of my work below. Thank you for looking over this problem. Where did I go wrong?
    Attached Images Attached Images

  4. #4
    Senior Member
    Join Date
    Jan 2012
    Posts
    2,339
    When you make the substitution [tex]u= v^2[/tex], you have dv= 2udu but you have treated it as if it were du= 2vdv.

    Instead, use the fact that [tex]\frac{u-1}{\sqrt{u}}= u^{1/2}- u^{-1/2}[/tex].

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