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    I've been stuck on this question for a while now, would appreciate it if anyone can help me on the following integral.
    Evaluate  \displaystyle\int^\frac{\pi}{2}_  0 [a+(a-1)cos(\theta)]^{-1}\ d\theta with  a > \frac{1}{2}
    I'm supposed to use a substitution of  t = tan(\frac{\theta}{2}) but I don't know why.
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    If you have a fraction with trig in the denominator, this substitution is often the way to go.

    I can send you a Powerpoint on the topic if you pm me with an email address.
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    What are the a's?
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    (Original post by limetang)
    What are the a's?
    The a's are constants that are greater than 1/2.
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    (Original post by JBKProductions)
    The a's are constants that are greater than 1/2.
    Okay I was just wondering whether or not they were a variable that was greater than a half. Which would probably make this very difficult to solve.
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    (Original post by limetang)
    Okay I was just wondering whether or not they were a variable that was greater than a half. Which would probably make this very difficult to solve.
    Hmmm...it doesn't actually say a is a constant but just a > 1/2 so i assumed it was....I doubt it would be a variable anyway but not too sure now.
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    (Original post by JBKProductions)
    I've been stuck on this question for a while now, would appreciate it if anyone can help me on the following integral.
    Evaluate  \displaystyle\int^\frac{\pi}{2}_  0 [a+(a-1)cos(\theta)]^{-1}\ d\theta with  a > \frac{1}{2}
    I'm supposed to use a substitution of  t = tan(\frac{\theta}{2}) but I don't know why.
    If you haven't received Mr M's powerpoint yet, try to manipulate t=\tan (\frac{\theta}{2}) to find an expression for \cos \theta and \dfrac{d\theta}{dt} in terms of t and then just carry out the substitution like any other you would do (don't forget to change your limits).

    Hint for finding \cos \theta - Notice that \tan 2\theta = \dfrac{2\tan \theta}{1+\tan ^2\theta}, therefore \tan \theta = \dfrac{2\tan \frac{\theta}{2}}{1+\tan ^2\frac{\theta}{2}} = \dfrac{2t}{1+t^2}.
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    See also http://en.wikipedia.org/wiki/Weierstrass_substitution
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    Thanks.
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    Just another question. If I have an integral that has trig in the denominator that isn't the standard arcsin, arccos or arctan integrals. Would the substitution of  t=tan(\frac{\theta}{2}) always work?
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    Which module is this from? Looks a bit harder than C4, which is all the core I've done to date. Teaching myself FP2 and FP3 is going to be a blast next year. >.<
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    (Original post by Jack-)
    Which module is this from? Looks a bit harder than C4, which is all the core I've done to date. Teaching myself FP2 and FP3 is going to be a blast next year. >.<
    I'm a first year undergraduate and this is one of my practice questions. Although this is probably in further maths but I have no idea which module it will be in. Sorry.
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    (Original post by Jack-)
    Which module is this from? Looks a bit harder than C4, which is all the core I've done to date. Teaching myself FP2 and FP3 is going to be a blast next year. >.<
    I did this at FP2 but I'm also doing it in my maths module of engineering at the moment.
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    (Original post by JBKProductions)
    I'm a first year undergraduate and this is one of my practice questions. Although this is probably in further maths but I have no idea which module it will be in. Sorry.
    Ah I see.
    (Original post by Kasc)
    I did this at FP2 but I'm also doing it in my maths module of engineering at the moment.
    Ah so its in FP2 then, thanks.

    How is maths at university in comparison to A levels (or anything equal)?
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    I'm not doing maths, and I'm only in my first year.

    It's basically A Level theory applied to more difficult problems and a hint of further maths.

    I imagine a maths degree would cover what I'm doing in one module only.
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    (Original post by Jack-)
    Ah I see.

    Ah so its in FP2 then, thanks.

    How is maths at university in comparison to A levels (or anything equal)?
    I find maths at university a lot harder than A levels, some lecturer's go really quick with the work and it's hard to keep up with it. The amount of work we get is a lot in comparison to a levels, we have loads of assessed and unassessed coursework. It's very independent, which is why I find it so much harder. I miss being spoon-fed.
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    Independent you say? Personally I'm really looking forward to that side of university, but maybe thats just because I dont know exactly how it will be!
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    You may like it. Some do some don't, I know I don't. But I do like the holidays, we get so much time off!
 
 
 
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