Help on an integration question? :)

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  1. tomo876's Avatar
    • New Member
    • Posts: 3
    Help on an integration question? :)
    hmm i know that:

    ∫ xcos2x

    = ((xsin2x)/2) + ((cos2x)/4)

    but then it asks, "Use your answer to find

    ∫x(cos^2)x

    any help would be much appreciated
  2. raheem94's Avatar
    • TSR Demigod
    • Posts: 5,512
    Re: Help on an integration question? :)
    (Original post by tomo876)
    hmm i know that:

    ∫ xcos2x

    = ((xsin2x)/2) + ((cos2x)/4)

    but then it asks, "Use your answer to find

    ∫x(cos^2)x

    any help would be much appreciated
    Remember,  \displaystyle  cos^2 x = \frac{cos2x+1}{2}

     \displaystyle \int xcos^2x \ dx = \int x \left( \frac{cos2x+1}{2} \right) \ dx =  \int \left( \frac{xcos2x}{2} + \frac{x}{2} \right) \ dx

    Now use the result of the previous part along with the new integration required.
  3. raheem94's Avatar
    • TSR Demigod
    • Posts: 5,512
    Re: Help on an integration question? :)
    (Original post by Brit_Miller)
    Try integration by parts
    Why integration by parts?

    He already has the result of  \int xcos2x \ dx, so i don't see any reason for it.
  4. Brit_Miller's Avatar
    • Benevolent Member
    • Location: Bristol
    • Posts: 694
    Re: Help on an integration question? :)
    (Original post by raheem94)
    Why integration by parts?

    He already has the result of  \int xcos2x \ dx, so i don't see any reason for it.
    Ignore me, I read it wrong, I thought it looked like something you could use a reduction formula for but had already posted and you can't delete it.
  5. raheem94's Avatar
    • TSR Demigod
    • Posts: 5,512
    Re: Help on an integration question? :)
    (Original post by Brit_Miller)
    Ignore me, I read it wrong, I thought it looked like something you could use a reduction formula for but had already posted and you can't delete it.
    Posts can be deleted.

    Just click on the edit button, you will see an option to delete.
  6. Brit_Miller's Avatar
    • Benevolent Member
    • Location: Bristol
    • Posts: 694
    Re: Help on an integration question? :)
    (Original post by raheem94)
    Posts can be deleted.

    Just click on the edit button, you will see an option to delete.
    Oh yeah, cheers, I didn't know that.
  7. tomo876's Avatar
    • New Member
    • Posts: 3
    Re: Help on an integration question? :)
    Thanks guys, exam is a week on Wednesday! But I'm much more worried about s2 than c4 haha
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