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Trapezoidal Rule

  1. Apr 10, 2013 #1
    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. jcsd
  3. Apr 11, 2013 #2

    Simon Bridge

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    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?
     
  4. Apr 11, 2013 #3
    " ... with n=20 ..."

    n = 40, not 20. That's the only thing I can see.'wrong'.
     
  5. Apr 11, 2013 #4

    Simon Bridge

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    It could be that simple.
     
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