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Math Help - Trig substitution or a different procedure?

  1. #1
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    Trig substitution or a different procedure?

    Solve:
    ∫√1+(2x-4)^2dx
    Hello everyone, I'm new to this so please bare with me. I'm not sure how to do this problem. I've thought maybe trig substitution but I've been unsuccessful in evaluating the problem. Now, I'm not asking for an answer, but any little bit of guidance/advice would be appreciated. Thanks everyone.

    -John
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  2. #2
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by zabooma87 View Post
    Solve:
    ∫√1+(2x-4)^2dx
    Hello everyone, I'm new to this so please bare with me. I'm not sure how to do this problem. I've thought maybe trig substitution but I've been unsuccessful in evaluating the problem. Now, I'm not asking for an answer, but any little bit of guidance/advice would be appreciated. Thanks everyone.

    -John

    Hi John! Welcome to the forum!

    I'll get you started and see if you can finish.

    \int \sqrt{1 + (2x - 4)^2} dx

    u = 2x-4
    du = 2 dx

    \frac{1}{2} \int \sqrt{u^2 + 1} du

    Notice that this is a trig substitution    x = a tan(\theta)

    \frac{1}{2} \int \sqrt{tan^2(\theta) + 1} \cdot sec^2(\theta) d\theta

    See what you can do from here! Good luck!
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