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Integration by parts trig substitution FP2 watch

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    (Original post by notnek)
    By the way this integral is beyond A Level Maths i.e. wouldn't be in an exam.
    Now you're making me sad and nostalgic - this used to be a 'standard' A level integral
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    (Original post by Dingooose)
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    \displaystyle \int e^{bx}cos(cx)dx = \frac {1} {b} e^{bx}cos(cx) + \frac {c} {b^2}e^{bx}sin(cx) - \frac {c^2} {b^2} \int cos(cx)e^{bx}dx

    \displaystyle \frac {c^2} {b^2} \int e^{bx}cos(cx)dx + \int e^{bx}cos(cx)dx = \frac {1} {b} e^{bx}cos(cx) + \frac {c} {b^2}e^{bx}sin(cx)

    Then we can factor out \displaystyle \int e^{bx}cos(cx)dx

    \displaystyle \int e^{bx}cos(cx)dx (\frac {c^2} {b^2} + 1) = \frac {1} {b} e^{bx}cos(cx) + \frac {c} {b^2}e^{bx}sin(cx)

    And the final step is division and putting in a constant of integration:

     \displaystyle \int e^{bx}cos(cx)dx=\frac{\frac{1}{b  }e^{bx}cos(cx)+\frac{c}{b^2}e^{b  x}sin(cx)}{\frac{c^2}{b^2}+1} + C
    That's correct And very impressive for a GCSE student.

    You can tidy it up a little bit more by multiplying top and bottom by b^2.
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    (Original post by davros)
    Now you're making me sad and nostalgic - this used to be a 'standard' A level integral
    It appears so much in this forum that it's hard to believe that it isn't an A Level integral.

    It might be the most common integral question asked here.
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    (Original post by notnek)
    That's correct And very impressive for a GCSE student.

    You can tidy it up a little bit more by multiplying top and bottom by b^2.
    Thanks! This totally beats my GCSE maths classes. They should bring calculus into the GCSE maths syllabus.
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    (Original post by Dingooose)
    Thanks! This totally beats my GCSE maths classes. They should bring calculus into the GCSE maths syllabus.
    Are you doing the Level 2 Further Maths course? It's a nice course for pre-A Level students who need a bigger challenge.

    I wish it existed back when I did GCSEs. Year 11 was a boring maths year for me.
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    (Original post by notnek)
    Are you doing the Level 2 Further Maths course? It's a nice course for pre-A Level students who need a bigger challenge.

    I wish it existed back when I did GCSEs. Year 11 was a boring maths year for me.
    Nah, my state school is kinda bad in some ways because they don't offer further maths GCSE or course of any kind. They do, however, offer a Level 3 Algebra course which I think I'm taking. And I want to take GCSE further maths somewhere because I already know quite a lot of the content as I've self-taught myself a lot of things.
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    (Original post by Dingooose)
    Nah, my state school is kinda bad in some ways because they don't offer further maths GCSE of any kind. They do, however, offer a Level 3 Algebra course which I think I'm taking.
    The Level 3 course is better than nothing but probably won't be much of a challenge if you're doing these kinds of integals.

    I assume you're learning A Level in your own time?
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    (Original post by notnek)
    The Level 3 course is better than nothing but probably won't be much of a challenge if you're doing these kinds of integals.

    I assume you're learning A Level in your own time?
    Yeah, I'm self teaching some stuff. Dabbled around with C1, C2, C3 and FP1 (proof by induction is by far my favourite topic from FP1), but I'm by no means an expert and I don't know these modules inside and out. Though I guess I am learning A level maths in my own time. I should probably worry about my other GCSE subjects a little bit more in truth.
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    (Original post by highestmountain)
    Could anyone help me with this?

    Find the integral of e^{xcosa} * cos(xsina) dx

    Supposedly I could use a substitution and take it from there but this one seems a little tricky.
    Any help appreciated!
    As this is fp2 you could also say that cos(x)=R(e^ix) then integrate using index laws and some rearrangement
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    (Original post by Gome44)
    As this is fp2 you could also say that cos(x)=R(e^ix) then integrate using index laws and some rearrangement
    Could you elaborate on this please? I'm very keen to know what you mean by cos(x)=R(e^ix).
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    (Original post by Dingooose)
    Could you elaborate on this please? I'm very keen to know what you mean by cos(x)=R(e^ix).
    The R stands for real part. I cba to latex the solution so I'll just link it from Wikipedia, see example 3
    https://en.m.wikipedia.org/wiki/Inte...er%27s_formula
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    (Original post by Gome44)
    The R stands for real part. I cba to latex the solution so I'll just link it from Wikipedia, see example 3
    https://en.m.wikipedia.org/wiki/Inte...er%27s_formula
    This method is pretty neat!
 
 
 
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