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Math Help - Approximate Integration - Trapezoidal Rule

  1. #1
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    Approximate Integration - Trapezoidal Rule

    42) Use the trapezoidal rule with n = 10 to approximate Integral (from 0 to 20) of cos(Pi*x)dx. Compare your result to the actual value. Can you explain the discrepancy?

    When I use the Trap Rule, I get Delta(x) = 20/10 = 2.

    So, 1(f(2) + 2f(4) + 2f(6) + 2f(8) + 2f(10) + 2f(12) + 2f(14) + 2f(16) + 2f(18) + f(20)) = 20.

    However, when I calculate the integral I get (1/Pi)*(Sin(Pi*x)) from 0 to 20, or just 0.

    I don't really know how to explain the discrepancy -- I only learned what trap. rule was yesterday!

    Any help? Am I right in the calculations?
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  2. #2
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    Quote Originally Posted by Sprintz View Post
    42) Use the trapezoidal rule with n = 10 to approximate Integral (from 0 to 20) of cos(Pi*x)dx. Compare your result to the actual value. Can you explain the discrepancy?

    When I use the Trap Rule, I get Delta(x) = 20/10 = 2.

    So, 1(f(2) + 2f(4) + 2f(6) + 2f(8) + 2f(10) + 2f(12) + 2f(14) + 2f(16) + 2f(18) + f(20)) = 20.

    However, when I calculate the integral I get (1/Pi)*(Sin(Pi*x)) from 0 to 20, or just 0.

    I don't really know how to explain the discrepancy -- I only learned what trap. rule was yesterday!

    Any help? Am I right in the calculations?
    Draw a graph of the function and indicate the positions of the knots (the points used in your calculation). Do you notice anything?

    Now try using the trap rule again with n=20.

    CB
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