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Math Help - Can someone help me solve this using substitution please?

  1. #1
    s3a
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    Can someone help me solve this using substitution please?

    I tried to get the detailed solution from Wolfram Alpha: http://www.wolframalpha.com/input/?i=integral+((tanx)^3)

    but, it uses the "reduction formula" which is something I have not learned yet not to mention that this question is in the "substitution" section of my text book.

    I was just hoping somebody could solve this for me using substitution because when I let u = tanθ, I get stuck and I can't see what else to do.

    Any help would be GREATLY appreciated!
    Thanks in advance!

    P.S.
    If you want to see my work, it is attached. This particular problem is the last one of the PDF and is #47.
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  2. #2
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    Quote Originally Posted by s3a View Post
    I tried to get the detailed solution from Wolfram Alpha: http://www.wolframalpha.com/input/?i=integral+((tanx)^3)

    but, it uses the "reduction formula" which is something I have not learned yet not to mention that this question is in the "substitution" section of my text book.

    I was just hoping somebody could solve this for me using substitution because when I let u = tanθ, I get stuck and I can't see what else to do.

    Any help would be GREATLY appreciated!
    Thanks in advance!

    P.S.
    If you want to see my work, it is attached. This particular problem is the last one of the PDF and is #47.
    \tan^3{t} = \tan{t} \cdot \tan^2{t} = \tan{t}(\sec^2{t} - 1) = \tan{t}\sec^2{t} - \tan{t}

    \int \tan{t}\sec^2{t} - \tan{t} \, dt = \int \tan{t} \sec^2{t} \, dt - \int \tan{t} \, dt

    can you finish?
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  3. #3
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    All you have to do is integrate for u and evaluate [F(b) - F(a)]

    (U^4)/4

    [F(√3) - F(-√3)]

    ...to solve it from your PDF work that is
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  4. #4
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    Quote Originally Posted by deathbycalc View Post
    All you have to do is integrate for u and evaluate [F(b) - F(a)]

    (U^4)/4

    [F(√3) - F(-√3)]

    ...to solve it from your PDF work that is
    the pdf work is incorrect.
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  5. #5
    s3a
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    @deathbycalc: my last step was incorrect because I still had du/dθ = (secθ)^2.

    @skeeter: I completed it and got the right answer but could you just check if it's not just a fluke please?
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  6. #6
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    Quote Originally Posted by s3a View Post
    @deathbycalc: my last step was incorrect because I still had du/dθ = (secθ)^2.

    @skeeter: I completed it and got the right answer but could you just check if it's not just a fluke please?
    for future reference, note that ...

    \int_{-a}^a (an \, odd \, function) \, dx = 0
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