trapezium rule question

https://www.mathsgenie.co.uk/resources/a-pure-trapezium-rule.pdf

i am doing question number 1. my exam board ocr mei states that the trapezium rule formula is this: 1/2h (y0 + yn) + 2(y1 + y2 + y3)

so i did this to work out question number one and got 14.619 units. mathgenie answers say that this is wrong and when i looked at the answers they are using a different formula: https://www.mathsgenie.co.uk/resources/a-pure-trapezium-ruleans.pdf

they seem to just be adding up all the y values without the bit in the middle (without multiplying the middle y values by 2). could someone help me understand which is the correct formula to use?

Reply 1

DFranklin

They're doing

\dfrac{1}{h}(\frac{1}{2}y_0 + y_1 + ... + y_{n-1} +\frac{1}{2}y_n)

Instead of

\dfrac{1}{2h}(y_0 +2 y_1 + ... + 2y_{n-1} +y_n)

(But the two formulae are obviously equivalent).

(edited 11 months ago)

Reply 2

pkchan

Original post by DFranklin

They're doing

\dfrac{1}{h}(\frac{1}{2}y_0 + y_1 + ... + y_{n-1} +\frac{1}{2}y_n)

Instead of

\dfrac{1}{2h}(y_0 +2 y_1 + ... + 2y_{n-1} +y_n)

(But the two formulae are obviously equivalent).
oh ok! thank you. i guess i just did it wrong with the formula i used then

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