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    Where am I going wrong? thank you
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    (Original post by otrivine)
    Where am I going wrong? thank you
    When you substituted u, you forgot to write your integral in terms of u. What you've actually said is

    \displaystyle  -4\int \sin^2 t \cos t \ dt = 4\int \sin t \cos t \ dt,

    which is clearly not correct.

    Try a substitution of \displaystyle  u=\sin t instead of \displaystyle  u=\cos t and post your working if you're still stuck.
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    (Original post by notnek)
    When you substituted u, you forgot to write your integral in terms of u. What you've actually said is

    \displaystyle  -4\int \sin^2 t \cos t \ dt = 4\int \sin t \cos t \ dt,

    which is clearly not correct.

    Try a substitution of \displaystyle  u=\sin t instead of \displaystyle  u=\cos t and post your working if you're still stuck.

    but its correct cause you use the identity of sin2x=2sinxcosx to get it into that form
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    (Original post by otrivine)
    but its correct cause you use the identity of sin2x=2sinxcosx to get it into that form
    You're not understanding what I'm getting at.

    Notice that from the line \displaystyle-4\int \sin^2 t \cos t \ dt

    to the line

    \displaystyle 4\int\frac{1}{2}\sin 2t \ dt

    you have used a substitution u=\cos t but your integral is still in terms of t.

    Think about how you normally use a substitution. You normally end up with an integral in terms of u if you use a u substitution right?


    This is how your working should read with a substitution u=\cos t:


    \displaystyle -4\int \sin^2 t \cos t \ dt = -4\int \sin^2 t \cos t \ \frac{dt}{du} \ du = 4\int \sin t\cos t \ du = ...


    Notice that there is a du on the RHS which is different to your working. I recommend you don't continue the working from here and use a u=\sin t sub instead.
 
 
 
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