A-level Mathematics/OCR/FP2/Complex Integration

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Midpoint Rule[edit]

The Midpoint Rule is more accurate than the Trapezium Rule. It works by finding the mid-points of rectangles drawn to the curve. The Midpoint Rule is:

Where: n is the number of strips.



Use the Midpoint Rule to evaluate using 4 strips.

Firstly, we work out h.

Now we begin to set up the Midpoint Rule.

Now we need to solve f(n)

As you can see the resultant from the midpoint rule is closer to the true value than the trapezium rule, but worse than Simpson's Rule.