math

posted by sam

the intergral

(10

4 (2x^2+3x+1)dx

i have to find the sum of the intergral using right and left endpts when n=3. I am confused on how to even start this or how to use these endpts.

  1. drwls

    What do you mean by the sum of the integral? Do you mean the value of the integral? Are the limits of integration 4 to 10? What is n? It does not appear in the mathematial expression you have written. Are you supposed to be doing a Simpson's Rule numerical integration with n=3 terms?

    That is what I assume they want you to do.

    The exact value of the integral is
    (2/3)x^3 + (3/2)x^2 +x evaluated at x=10, minus the value at x = 4. This is
    826.67 - 70.67 = 756

    Using Simpson's rule with 3 terms and h=3 as the interval width, I get
    (h/3)[f(4) + 4 f(7) + f(10)]
    = 1*[45 + 480 + 231) = 756

    The agreement is perfect because the curve is a parabola, and Simposn's rule provides a parabolic best fit to each interval.

  2. sam

    Find the Riemann sum for this integral using right and left endpoints and n=3. when i type in 756 it shows to be the wrong answer.

  3. drwls

    You left out the word Riemann before; so I solved the wrong problem.

    The Riemann sum is defined here:
    http://en.wikipedia.org/wiki/Riemann_integral
    It is a less accurate approxiation to the integral than Simpson's rule. I will leave you to calculate it.

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