Simpsons Rule Help! (1 Viewer)

[Relish9]

Use Simpson's Rule with 5 function values to find an approximate value of ∫(x^3 - 1).dx from x = 1 and x = 0.

I know the formula about h/3 (first + last + 4odds + 2evens) but I don't know how to get the right answer, I keep getting it wrong. The answer is - 0.75.

 

[Coookies]

Is that -0.75? Because area can't be negative.

Ive tried the question and I got 0.74479...

 

[mathaesthetics]

its 2 odd 4 even isnt it?

 

[D94]

It's 4 times the even, and 2 times the odd, except first and last. So: 1, 4, 2, 4, 1. You can tell because it is split up into groups of 1, 4, 1, and when the last is overlapped with the first, you add 1 + 1 = 2, so you get 1, 4, 2, 4, 1.

 

[D94]

Is that -0.75? Because area can't be negative.

Ive tried the question and I got 0.74479...

Yes, the answer is -0.75. We are finding the area which is below the x-axis. If you simply integrate it, you can verify the result.

h = 1/4 and you split it up into 0, 1/4, 1/2, 3/4, 1. Just applying the simple formula yields the result -0.75.

 

[Carrotsticks]

NOTE: The formula can be different, depending on if you consider there to be a y_0 or not.


If you make your first term y_0, then the formula is:



or in other words:



BUT if you make y_1 your first term, then the formula is:



or in other words:

 

[Coookies]

Thank god, I thought I've used the wrong formula all this time!