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    Hi

    I'm revising for the Edexcel C4 exam on Monday and covering integration at the moment. In my book it has an extension part containing:

    integrals of the type S sinax cosbx dx
    e.g S sin5x cos3x dx

    and integrals of the type sec^n x tanx dx

    do we need to know this ?

    thanks
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    If it's in the book, then I would expect so. But you can check the syllabus online if you want to.
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    no mention in the syllabus on the website

    just wondering why they've mentioned it in the book
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    I suppose \displaystyle\int\sin (ax)\cos (bx) dx could come under "Students are expected to be able to use trigonometric identities to integrate, for example, sin2 x, tan2 x, cos2 3x."

    And the other one is integration by substitution: "Except in the simplest of cases the substitution will be given." I'm not sure if this is included in "the simplest cases," but I see no reason why they couldn't ask it.
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    thanks

    the way they explain it in the book involves factor formulae which we are not given and were never told to learn

    sin(A+B) + sin(A-B) = 2sinAcosB

    which makes me think it might just be extension


    this type of question doesnt involve substitution though does it?
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    The factor formulae can be derived from
    \begin{array}{cl}\sin (a+b) &= \sin a\cos b +\sin b\cos a \\ \sin (a-b) &= \sin a\cos b -\sin b\cos a \\ \Rightarrow \sin(a+b) +\sin(a-b) &= 2\sin a \cos b \end{array}
    But they might give you this identity anyway. I think it's in the formula booklet too. [edit: well it isn't, but a form of it is.]

    The other one is integration by substitution (substitute u=sec x , du/dx = sec x tan x ).
 
 
 
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