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Integration by parts with a 3rd term edexcel c4 watch

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    a) integrate xsin(2x)

    did this part fine, answer is -1/2xcos(2x) + 1/4sin(2x) +C

    b) given y=0 when x= 1/4pi, solve dy/dx = xsin(2x)cos^2(y)

    I realise I must be missing some trick, should probably have just paid attention in class, any help would be great.
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    (Original post by jameshegarty)

    b) given y=0 when x= 1/4pi, solve dy/dx = xsin(2x)cos^2(y)
    Separable:

    \displaystyle

\begin{equation*}\frac{\mathrm{d  }y}{\mathrm{d}x} = x\sin x\cos^2 y \Rightarrow \int \frac{1}{\cos^2 y} \, \mathrm{d}y = \int x\sin 2x \,\mathrm{d}x\end{equation*}

    You know how to integrate the RHS from part(a), the LHS is \frac{1}{\cos^2 y} = \sec^2 y which you should know integrates to...?
    Spoiler:
    Show
    What does \tan x differentiate to?
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    (Original post by Zacken)
    Separable:

    \displaystyle

\begin{equation*}\frac{\mathrm{d  }y}{\mathrm{d}x} = x\sin x\cos^2 y \Rightarrow \int \frac{1}{\cos^2 y} \, \mathrm{d}y = \int x\sin 2x \,\mathrm{d}x\end{equation*}

    You know how to integrate the RHS from part(a), the LHS is \frac{1}{\cos^2 y} = \sec^2 y which you should know integrates to...?
    Spoiler:
    Show
    What does \tan x differentiate to?
    loooooooooool, im a massive idiot. safe
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    (Original post by jameshegarty)
    loooooooooool, im a massive idiot. safe
    Awesome.
 
 
 
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Updated: March 8, 2016
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