A-Level Maths: I3-02 Numerical Integration: Estimating using Trapeziums

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This may just be a coincidence, but when using rectangles, you get 3.75 as the underestimate and 5.75 as the overestimate. When taking the average of these results you get 4.75, which is the same area estimated using trapeziums. Just wondering whether this is a general rule, or just a coincidence for this example?

jamminermit
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When would this be useful in a real life scenario? I see why root location is important but is there ever a situation where integration is too difficult?

harrysmith