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Thread: integration by substitution

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    Cadet
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    integration by substitution

    Consider the integral of sin(2x+1).
    I note the normal method would be to let u=2x+1(if you are asked to use substitution).
    But can someone explain the following method:
    integral (sin(2x+1)dx)=integral(sin(2x+1) d(2x+1)/2)?

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    Senior Member integral95's Avatar
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    Re: integration by substitution

    I take that you mean this



    We know that is 1 so they basically subbed that 1 into the integral in the right hand side.

    Using the Substitution , you sub it into the equation and cancel things out with the chain rule like this



    That's how it works, but no 3U student would get taught like that.
    Last edited by integral95; 22 Nov 2017 at 10:39 AM.
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    Split arrowhead ichila101's Avatar
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    Re: integration by substitution

    Yeah but as 'integral95' said thats a bull crap half assed answer that wont be asked to 3 unit students

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