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Trapezium Rule Question

Hi there, we have just started the Trapezium Rule in class and I have tried to complete some extra questions at home for revision. However I have attempted one and got the wrong answer. If someone could show me the working out I would appreciate it. Thanks :smile:.

'Use the Trapezium Rule with ordinates at x=1, x=2 and x=3 to estimate the value of ∫(top 3, bottom 1) √40-x^3 dx'
you need to find the height first by using h=(b-a)/2 so h=(3-1)/2 and so h=1.5

then find the y values by using the x values they already give you
so when x=1, y=√39 when x=2, y=4√2 and when x=3, y=√13

therefore
Area = 0.5 x 1.5 x (√39 + 2(4√2) +√13)
Area = 0.75 x 21.16.....
Area = 15.873
Area = 15.9 (3 s.f)

I think (and hope) that's right :smile:
Original post by wajeeh1364
you need to find the height first by using h=(b-a)/2 so h=(3-1)/2 and so h=1.5

then find the y values by using the x values they already give you
so when x=1, y=√39 when x=2, y=4√2 and when x=3, y=√13

therefore
Area = 0.5 x 1.5 x (√39 + 2(4√2) +√13)
Area = 0.75 x 21.16.....
Area = 15.873
Area = 15.9 (3 s.f)

I think (and hope) that's right :smile:


how is h = 1.5?
because surely h = 1 as 3-1 = 2 and 2/2 = 1??
I got therefore an answer of

area = (1/2)(1)x[(√39 + √13 + 2(4√2)]
= 1/2 x (21.1641577...)
= 10.5821..
= 10.6 (3s.f.)
Original post by Justtryingtolive
how is h = 1.5?
because surely h = 1 as 3-1 = 2 and 2/2 = 1??
I got therefore an answer of

area = (1/2)(1)x[(√39 + √13 + 2(4√2)]
= 1/2 x (21.1641577...)
= 10.5821..
= 10.6 (3s.f.)


Oh yeah..😅 Silly mistake
Reply 4
Avatar for aadil10
aadil10
13
Original post by F Edexcel
Just write pizza Hut because a trapezium is a pizza hut sign , so they will give you the mark, thats what examiners are looking for.To see whether you understand the quesiton.


It's all about getting you to think outside the box, or in this case trapezium.

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