Rectangles FP2

Q1 of this paper: http://www.ocr.org.uk/Images/66647-question-paper-unit-4726-01-further-pure-mathematics-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-question-paper-unit-4726-01-further-pure-mathematics-2.pdf

Update: Link to MS: http://pmt.physicsandmathstutor.com/download/Maths/A-level/FP2/Papers-OCR/June%202009%20MS%20-%20FP2%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)

Thanks for this! any way I can do it on the calculator, it keeps saying augmentation error. Also are the values in Radians?

Thanks