Trap. Rule Question (1 Viewer)

[chingyloke]

find [ordinates 2-0] (x-x^2) dx with the trapezoidal rule using 4 trapezia...can anybody help? i keep getting stuck.

 

[lyounamu]

find [ordinates 2-0] (x-x^2) dx with the trapezoidal rule using 4 trapezia...can anybody help? i keep getting stuck.

well using 4 trapezia means using 5 ordinates.

so the ordinates should be 0, 0.5, 1, 1.5 and 2.

Value = (Appr) 0.5/2 (0 + 0.25 x 2 + -1.5 + -2) = -3/4

If you are finding the area:
However, if you draw the diagram you will see that half of the diagram is under the x-axis meaning that you should use the absolute value on that to find the area. (I will call that area under x-asis, A2 and A1 is ABOVE the x-axis)

A1 = (appr) 0.5/2 (0 + 0.25 x 2 + 0) = 1/8

A2 = (appr) 0.5/2 (0 -0.75 x 2 -2) = -7/8

But using absolute value on A2, you get 7/8 as the area.
So total area = 1/8 + 7/8 = 1

 

[chingyloke]

okay. thankyou. yeh wasn't sure to use absolute values or not.

but the question isn't specifically asking for area...should i be using absolutes then?

 

[lyounamu]

okay. thankyou. yeh wasn't sure to use absolute values or not.

but the question isn't specifically asking for area...should i be using absolutes then?

oh, i don't think so.

 

[PC]

x******f(x)***W*****P
0.0***0.000***1*****0.000
0.5***0.250***2*****0.500
1.0***0.000***2*****0.000
1.5***-0.750**2*****-1.500
2.0***-2.000**1*****-2.000
*******************--------
*******************-3.000

Integral = 1/2 x h x sum
= 1/2 x 0.5 x –3
= –0.75

But it's not a well written question. Trapezoidal rule (and Simpson's rule) are practical ways of approximating areas, so this probably should be done in parts. The area by trapezoidal rule, is actually 1 u².

 

[lyounamu]

x******f(x)***W*****P
0.0***0.000***1*****0.000
0.5***0.250***2*****0.500
1.0***0.000***2*****0.000
1.5***-0.750**2*****-1.500
2.0***-2.000**1*****-2.000
*******************--------
*******************-3.000

Integral = 1/2 x h x sum
= 1/2 x 0.5 x –3
= –0.75

But it's not a well written question. Trapezoidal rule (and Simpson's rule) are practical ways of approximating areas, so this probably should be done in parts. The area by trapezoidal rule, is actually 1 u².

Yes, I agree. It's quite a poorly written question...

That's why I wrote two solutions even though I think the first one is more correct.

 

[Makro]

Well isn't trap + simpsons rule used to find approximations of AREA? So you'd assume that its always asking for area?

 

[lyounamu]

Well isn't trap + simpsons rule used to find approximations of AREA? So you'd assume that its always asking for area?

Well no.

For this question, this is just asking for the value that you get out of this.

I know that the wording of this question is extremely ambiguous and really different in nature, we have to do what is asked.

Since they didn't ask for area, (they didn't specify it) so we just put the value that we get.

 

[chingyloke]

yeah well that was the question in the assessment...

perhaps i should write both down.

anyway. thanks heaps for your help guys.