# Trapezoidal Rule

1. Apr 10, 2013

### mxthuy95

1. The problem statement, all variables and given/known data

Determine and evaluate a definite integral for which (1/40( (0)^3 + 2(.05)^3 +2(.1)^3 +.... 2(1.95)^3 + (2)^3 )) is a trapezoidal approximation. Which is greater, the integral or trapezoidal approximation why

2. Relevant equations

3. The attempt at a solution

So i figure that the the original equation is x^3 and the limits are 0 to 2 so i got this integral

2
∫ X^3 = 4.0025 using trapezoidal rule with n=20 on my Riemann sum program. I said that this is
0

greater than the actual integral because the graph is increasing and concave up. I check with my

teacher and it was wrong. So where did i go wrong.

Thank you.

2. Apr 11, 2013

### Simon Bridge

That's what I'd have said too.
Have you correctly identified the function being integrated?
Have you use the correct reasoning?

... that would be: $$\frac{1}{40}\left ( 0^3+2(0.05)^3+2(0.1)^3+\cdots + 2(1.95)^3+(2.0)^3 \right )$$

Compare with the trapezoidal rule:
$$\int_a^b f(x)dx \approx \frac{b-a}{2N}\left ( f(x_1)+2f(x_2)+\cdots +2f(x_{N-1})+f(x_N) \right )$$... I'm having trouble faulting this.
Perhaps the teacher means something else?

3. Apr 11, 2013

### TheoMcCloskey

" ... with n=20 ..."

n = 40, not 20. That's the only thing I can see.'wrong'.

4. Apr 11, 2013

### Simon Bridge

It could be that simple.