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Math Help - Trig. substitution

  1. #1
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    Trig. substitution

    Greetings,

    How is the integral (file attached) solved?

    Correction: the integrand should be squared, as it equals x^2

    I am aware of the pythagorian identities (cos^2x + sin^2x = 1, thus cos^2x = 1 - sin^2x). I have solved an integral with just a dx in the numerator but I have never solved an integral with an x^2 in the numerator. I don't what to do with it.

    Sincere regards /

    KaemperTrig. substitution-scan_marts-27-2014-11-40-48-194-am.png
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  2. #2
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    Re: Trig. substitution

    You didn't do it correctly. The substitution here is easy, it's the trig that gets to be a mess.

    Try the substitution $x=3\sin(u)$ and be careful with the trig.
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  3. #3
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    Re: Trig. substitution

    Thank you this answer.

    I have a new integral (Trig. substitution-scan_marts-27-2014-11-05-07-641-pm.png) (this time thoroughly computed). Still it is not correct, what is wrong?
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  4. #4
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    Re: Trig. substitution

    you haven't finished it is what isn't correct.

    you are still at $\int (3 \sin(u))^2 ~du$

    You can expand out the trig term and continue.
    Thanks from kaemper
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  5. #5
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    Re: Trig. substitution

    It is done correctly now.
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