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Urgent help C4 trig addition formulae & integration Watch

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    Hi I'm really stuck on this particular question:

    Evaluate exactly the integral:

    Integral sign with limits 2pi/3 and pi, then the expression is 1/2sin(theta-(pi/3)).
    I'm thinking of converting it into a log expression like ln 2sin(theta-(pi/3)) ???

    Would appreciate some help please!
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    (Original post by jordanwu)
    Hi I'm really stuck on this particular question:

    Evaluate exactly the integral:

    Integral sign with limits 2pi/3 and pi, then the expression is 1/2sin(theta-(pi/3)).
    I'm thinking of converting it into a log expression like ln 2sin(theta-(pi/3)) ???

    Would appreciate some help please!
    The derivative of things like sin(x-pi/2), you just need to apply the chain rule and you get cos(x-pi/2).

    Does that help you with your integral?
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    Hi I don't see how differentiating can help with the integral :/ I know 2sin(theta-(pi/3)) differentiates to 2cos(theta-(pi/3)) but can't see what to do next..
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    (Original post by SeanFM)
    The derivative of things like sin(x-pi/2), you just need to apply the chain rule and you get cos(x-pi/2).

    Does that help you with your integral?
    Hi I don't see how differentiating can help with the integral :/ I know 2sin(theta-(pi/3)) differentiates to 2cos(theta-(pi/3)) but can't see what to do next..
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    (Original post by jordanwu)
    Hi I don't see how differentiating can help with the integral :/ I know 2sin(theta-(pi/3)) differentiates to 2cos(theta-(pi/3)) but can't see what to do next..
    Differentiating and integrating are the reverse of eachother. It's supposed to be an indirect hint.

    Using what you've just said, what do you think (1/2) * sin(theta-(pi/3)) integrates to?
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    (Original post by SeanFM)
    Differentiating and integrating are the reverse of eachother. It's supposed to be an indirect hint.

    Using what you've just said, what do you think (1/2) * sin(theta-(pi/3)) integrates to?
    1/2 * (-cos(theta-(pi/3))?? Sin integrates to -cos right?
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    (Original post by jordanwu)
    1/2 * (-cos(theta-(pi/3))?? Sin integrates to -cos right?
    Yes, well done.
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    (Original post by SeanFM)
    Yes, well done.
    So I just sub in the limits into that, simplify then I'm done?
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    (Original post by jordanwu)
    So I just sub in the limits into that, simplify then I'm done?
    You've got your expression for the integral so I don't see why not
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    (Original post by SeanFM)
    You've got your expression for the integral so I don't see why not
    Ok thanks for the help, much appreciated
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    (Original post by jordanwu)
    Ok thanks for the help, much appreciated
    No worries.
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    (Original post by SeanFM)
    No worries.
    Hey sorry to bother you again but can 1/2 be taken out of the integral sign? As the expression is 1/(2*sin(theta-(pi/3)))
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    (Original post by jordanwu)
    Hey sorry to bother you again but can 1/2 be taken out of the integral sign? As the expression is 1/(2*sin(theta-(pi/3)))
    Ah, it is a case of ambiguous equations then it wasn't clear that 1/2sin(theta-(pi/3)) is 1/(2*sin(theta-(pi/3)).

    1/2 can be taken out to give (1/2) * the integral of (1/(sin(theta-(pi/3)))).

    What would that integral be?
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    (Original post by SeanFM)
    Ah, it is a case of ambiguous equations then it wasn't clear that 1/2sin(theta-(pi/3)) is 1/(2*sin(theta-(pi/3)).

    1/2 can be taken out to give (1/2) * the integral of (1/(sin(theta-(pi/3)))).

    What would that integral be?
    Isn't it ln when you've integrating 1/something?
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    (Original post by SeanFM)
    Ah, it is a case of ambiguous equations then it wasn't clear that 1/2sin(theta-(pi/3)) is 1/(2*sin(theta-(pi/3)).

    1/2 can be taken out to give (1/2) * the integral of (1/(sin(theta-(pi/3)))).

    What would that integral be?
    Or would it be 1/2 * (cos(theta-(pi/3))?
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    (Original post by jordanwu)
    Isn't it ln when you've integrating 1/something?
    That is what it seems like you are integrating, but it is unclear.

    Please use latex if you can, or post a picture of the question, or type it out in a more understandable way as I do not know what the question is.
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    (Original post by SeanFM)
    That is what it seems like you are integrating, but it is unclear.

    Please use latex if you can, or post a picture of the question, or type it out in a more understandable way as I do not know what the question is.
    Name:  image.jpg
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    Sorry about the shadow xD
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    (Original post by jordanwu)
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    Sorry about the shadow xD
    Great :borat:

    So yes, you can take the half outside of the integral and that leaves you with (1/sin(...)). What's the integral of that?
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    (Original post by jordanwu)
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    Sorry about the shadow xD

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    (Original post by jordanwu)
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    Sorry about the shadow xD
    You can write that as \displaystyle \frac{1}{2} \int_{2\pi/3}^{\pi} \text{cosec}{\left(\theta - \frac{\pi}{3}\right)} \, \mathrm{d}\theta and then look in your formula book for what cosec x integrates to.
 
 
 
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