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Math Help - Integrals...please...help

  1. #1
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    Integrals...please...help

    Hi,
    Im new!I have been having trouble with this calculus stuff in general, but integrals have tripped me up wayyy more than derivatives and i need major help!

    okay so here is the problem im stuck on

    INTEGRATE: (1-sin23t) cos 3t dt

    so do i substitute or do i do some other math thingy?

    Sorry for my ignorance,

    Thanks in Advanced
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  2. #2
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    Re: Integrals...please...help

    Quote Originally Posted by IgnorantMathGuru View Post
    Hi,
    Im new!I have been having trouble with this calculus stuff in general, but integrals have tripped me up wayyy more than derivatives and i need major help!

    okay so here is the problem im stuck on

    INTEGRATE: (1-sin23t) cos 3t dt

    so do i substitute or do i do some other math thingy?

    Sorry for my ignorance,

    Thanks in Advanced
    you should know another form of $1-\sin^2(3t)$ that would be convenient for this problem.

    once you figure that out the integral should be simple
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  3. #3
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    Re: Integrals...please...help

    is the answer 1/3 sin 3t+c

    because my answer key looks like its saying something different
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  4. #4
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    Re: Integrals...please...help

    Quote Originally Posted by IgnorantMathGuru View Post
    is the answer 1/3 sin 3t+c

    because my answer key looks like its saying something different
    no that's not the answer
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  5. #5
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    Re: Integrals...please...help

    is this the answer:
    1/3sin3t-1/9 sin^3t+c

    if so....can... you help me get to that answer maybe?
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  6. #6
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    Re: Integrals...please...help

    Quote Originally Posted by IgnorantMathGuru View Post
    is this the answer:
    1/3sin3t-1/9 sin^3t+c

    if so....can... you help me get to that answer maybe?
    $\displaystyle{\int}\left(1-\sin^2(3t)\right)\cos(3t)~dt$

    $u=\sin(3t)$

    $du=3\cos(3t)dt$

    $\displaystyle{\int}(1-u^2)~\dfrac {du} 3$

    $\dfrac 1 3 \left(u-\dfrac{u^3}{3}\right)+C$

    $\dfrac 1 3 \left(\sin(3t)-\dfrac{\sin^3(3t)}{3}\right)+C$
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