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 .

'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'

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 .

'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'

Just followed the steps I had done before. I'm normally great at making glaring errors though haha. Thanks again in advance.

You have the strip number wrong. If we are using 3 values, we have 2 strips (draw a graph and you will see that you have 2 trapeziums).

So what is it I am changing?

Your $h$ should be $h = \frac{3-1}{2} = 1$.

So what is it I am changing?

If you draw a sketch like this all the time, it is invaluable. $h$ is the number of strips you have, and if you have three numbers, you get two strips, as below:

Would the curve have to be exact or just a sketch?

Just any random sketch, the curve I drew is some random piece of crap I drew up in paint, it doesn't look anything like the actual graph but it's just there to remind me of how many strips there are.

Ah great, I'll keep that in mind for the future. Thanks again for your help.