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# Can someone please explain the trapezium rule? watch

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1. Hi guys. We went through the trapezium rule very briefly one lesson just before the end of term and I never quite grasped it. The teacher said it was easy, which it probably is, but when I tried an exam Q on it I didn't have a clue. I have attatched the question I am stuck on. Is there someone that can explain part b) please. Cheers
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2. ½(a+b)h

is the rule...a+b being the two parallel sides and h being the side perpendicular to both.
3. That is for one trapezium, the extended version is:

h/2(x0 + 2(x1) + 2(x2) + 2(x3) + x4)

where h = (7.06 - 6.06)/2 = 0.5

x0, x1, x2 etc... are replaced by the numbers in the corresponding positions in the row of numbers you have worked out. You do not double the first and last numbers, just the middle group.
This is the way I have learnt it anyways

W.
4. Actually h is worked out from the x row

so, according to my book it would be (1.5-0.5)/4 (4 is the number of intervals)

so h = 0.25

I think...
5. (Original post by wonderboy)
Actually h is worked out from the x row

so, according to my book it would be (1.5-0.5)/4 (4 is the number of intervals)

so h = 0.25

I think...
yeah, so basically the difference between each interval
6. yes, just remember it as

the integral or area approx. = half width multiply( first +the last +twice the rest)
7. Just think of estimating the area beneath a curve with LOADS of stupid trapeziums. You only multiply the middle values by two, as you use these lengths in ALL the central trapeziums. The two outermost lines are used only once, due to them being at the end of your bound.

h(difference between x values) divided by two gives... h/2.

h/2(y1x1 + ya/b/cx2 + last y value x 1)

This area is an ESTIMATE, so say, equals approximately...

Hope my notation wasnt HORRID.
8. could someone explain to me how the number of calculations are affected by (and the meaning of):

1 no of Intervals
2 no of ordinates
9. Ordinates is the number of x values... Your interval number is always ordinates take away 1. You always use intervals when finding h, and use ordinates in the table. Hope that made sense...

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