# Simpson's Rule Question! Very hard!

#### coolhacker

Hi

Simpson's Rule i dont understand anything. its really hard.

1. A vehicle starts from rest and its velocity is measured every 8 seconds, with values as follows:

Time t (s) =Velocity v (ms-1)
0 = 0
1.0 =0.4
2.0 =1.0
3.0 =1.7
4.0 =2.9
5.0 =4.1
6.0 =6.2
7.0 =8.0
8.0 =9.4

The distance traveled in 8.0 seconds is given by

[FONT=&quot] 8.0 ON THE TOP AND 0 ON THE BOTTOM SORRY ABOUT THE CONFUSION
[/FONT]

vdt. Estimate this distance using simpson's rule, giving your answer to 3 significant figures.

thank you very much

#### undefined

MHF Hall of Honor
Hi

Simpson's Rule i dont understand anything. its really hard.

1. A vehicle starts from rest and its velocity is measured every 8 seconds, with values as follows:

Time t (s) =Velocity v (ms-1)
0 = 0
1.0 =0.4
2.0 =1.0
3.0 =1.7
4.0 =2.9
5.0 =4.1
6.0 =6.2
7.0 =8.0
8.0 =9.4

The distance traveled in 8.0 seconds is given by

[FONT=&quot] 8.0 ON THE TOP AND 0 ON THE BOTTOM SORRY ABOUT THE CONFUSION
[/FONT]

vdt. Estimate this distance using simpson's rule, giving your answer to 3 significant figures.

thank you very much
Simpson's rule is an approximation, and basically there is a formula and all you have to do is plug in numbers.

For this problem I would think the question designer might ask for the composite Simpson's rule because of the number of data points, but since this is not explicitly asked for, I would just go with ordinary Simpson's rule.

You do have some reference material to give you the formula, right? It's on Wikipedia too.

• mr fantastic and HallsofIvy

#### HallsofIvy

MHF Helper
No, problems involving Simpson's rule are NOT hard. It is simply a matter of memorizing Simpson's rule (or knowing where to look it up- I'll bet it's in your textbook) and then plugging in numbers.

Simpson's rule says that
$$\displaystyle \int_a^b f(x) dx= \frac{b-a}{3}(f(x_0)+ 4f(x_1)+ 2f(x_2)+ 4f(x_3)+ \cdot\cdot\cdot$$$$\displaystyle + 2f(x_{n-2})+ 4f(x_{n-1})+ f(x_n))$$ where $$\displaystyle x_0= a$$, $$\displaystyle x_n= b$$ and the $$\displaystyle x_i$$ are equally spaced between a and b (that is, $$\displaystyle x_i- x_{i-1}= \frac{b-a}{n}$$). In order to make the "4", "2" alternation work out, there must be an odd number of points (n even since we start counting at 0).

In this particular problem, you have 9 points with n= 8. a= 0, b= 8.0 so b- a= 8.0.
$$\displaystyle \frac{8}{3}(0+ 4(.4)+ 2(1.0)+ 4(1.7)+ 2(2.9)+ 4(4.1)+ 2(6.2)+ 4(8.0)+ 9.4)$$

• mr fantastic