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Math Help - A Trig Integral

  1. #1
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    A Trig Integral

    Hi everyone. I did a trig integral problem. Can someone please check my work for me? Thanks.

     \int sin(3x)^3cos(3x)


    <br /> <br />
u=sin(3x) du=cos3x dx<br /> <br />

     \int u^3 du


    u^4/4+c

     sin(4x)^4/4+c


    Thanks a lot, everyone!
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  2. #2
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    Quote Originally Posted by zhangxupage2 View Post
    [FONT=Verdana]Hi everyone. I did a trig integral problem. Can someone please check my work for me? Thanks.

     \int sin(3x)^3cos(3x)


    <br /> <br />
u=sin(3x) du=cos3x dx<br /> <br />
\int u^3 du<br /> <br />
 u^4/4+c<br /> <br />
sin(4x)^4/4+c<br />

    Thanks a lot, everyone!
    du=3\cos{(3x)}dx
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  3. #3
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    Thanks a lot. I thought I made a mistake.
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  4. #4
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    Here's my revised answer

    u=sin(3x) du=3cos(3x)dx

    <br />
\int  u^3 du/3<br />

    u^4/4*1/3

    sin(3x)^4/12+c

    Is this correct?
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  5. #5
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    Quote Originally Posted by zhangxupage2 View Post
    Here's my revised answer

    u=sin(3x) du=3cos(3x)dx

    <br />
\int  u^3 du/3<br />

    u^4/4*1/3

    sin(3x)^4/12+c

    Is this correct?
    Correct
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  6. #6
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    Thanks a lot.
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