The Student Room Group

Simpson/Trapezium rule terms

What's the value for each term in these rules? I'm given:

Trapezium rule:
I=12[f(x0)+f(x0+Δx)]ΔxI=\dfrac{1}{2}[f(x_0)+f(x_0+\Delta x)]\Delta x

Unparseable latex formula:

\displaystyle I=\left[f(a)+2\sum^{N-1}_{i]\dfrac{\Delta x}{2}



Simpson's Rule:
I=Δx3[f(x0)+4f(x0+Δx)+f(x0+2Δx)]I=\dfrac{\Delta x}{3}[f(x_0)+4f(x_0+\Delta x)+f(x_0+2\Delta x)]

I=Δx3[f(a)+4f(a+Δx)+2f(a+2Δx)+4f(a+3Δx)+...+2f(a+[n2]Δx)+4f(a+[n1]Δx)+f(b)]I=\dfrac{\Delta x}{3}[f(a)+4f(a+\Delta x)+2f(a+2\Delta x)+4f(a+3\Delta x)+...+2f(a+[n-2]\Delta x)+4f(a+[n-1]\Delta x)+f(b)]

I thought the it's just the non sum formula but with numbers (I need to find the "Trapezium/Simpson's rule terms" for each value of I from 0-256), but my instructions seem to disagree and refers me to the sums, how there's two different types of term in the trapezium rule and three in Simpson's rule and so there needs to be two/three different formulae depending on the value of I, which I don't really see...

Quick Reply

Latest