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    Q1 of this paper: http://www.ocr.org.uk/Images/66647-q...hematics-2.pdf

    So I know that it is an increasing function, so to find the upper bound I should find the integral of Ln(cos x) from n+1 to 1. The mark scheme does it a different way and I just don't understand it so can someone help.

    Thanks

    Link to MS : http://pmt.physicsandmathstutor.com/...0FP2%20OCR.pdf
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    (Original post by ChemBoy1)
    Q1 of this paper: http://www.ocr.org.uk/Images/66647-q...hematics-2.pdf

    So I know that it is an increasing function, so to find the upper bound I should find the integral of Ln(cos x) from n+1 to 1. The mark scheme does it a different way and I just don't understand it so can someone help.

    Thanks

    Link to MS : http://www.ocr.org.uk/Images/66647-q...hematics-2.pdf
    You have linked to the question paper twice. Could you republish the link to the MS?
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    Update: Link to MS: http://pmt.physicsandmathstutor.com/...0FP2%20OCR.pdf

    Thanks Old Engineer
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    (Original post by ChemBoy1)
    Update: Link to MS: http://pmt.physicsandmathstutor.com/...0FP2%20OCR.pdf

    Thanks Old Engineer
    The upper bound is clearly just the sum of the areas of the rectangles since those cover more area than the curve up to the x-axis.

    This is precisely what the mark scheme shows, \displaystyle \sum 0.3y means summing up the areas of the rectangles where 0.3 is the base (same for all rectangles), and y is the height which depends on the function's value.

    Here,

    \displaystyle \sum 0.3y = 0.3\ln \cos 0.3 + 0.3\ln \cos 0.6 + 0.3\ln \cos 0.9 + 0.3\ln \cos 1.2 + 0.3\ln \cos 1.5 \approx -1.313

    as required (though turn it +ve since area is +ve by definition)
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    Thanks for this! any way I can do it on the calculator, it keeps saying augmentation error. Also are the values in Radians?

    Thanks
    (Original post by RDKGames)
    The upper bound is clearly just the sum of the areas of the rectangles since those cover more area than the curve up to the x-axis.

    This is precisely what the mark scheme shows, \displaystyle \sum 0.3y means summing up the areas of the rectangles where 0.3 is the base (same for all rectangles), and y is the height which depends on the function's value.

    Here,

    \displaystyle \sum 0.3y = 0.3\ln \cos 0.3 + 0.3\ln \cos 0.6 + 0.3\ln \cos 0.9 + 0.3\ln \cos 1.2 + 0.3\ln \cos 1.5 \approx -1.313

    as required (though turn it +ve since area is +ve by definition)
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    (Original post by ChemBoy1)
    Thanks for this! any way I can do it on the calculator, it keeps saying augmentation error. Also are the values in Radians?

    Thanks
    Yes you need to be in radians for this.

    Not sure what that error means, but you can simply type in \displaystyle 0.3 \sum_{n=1}^{5} \ln(\cos(0.3n)) on your calc to give it straight away.
 
 
 
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