I'm a little confused with this integration problem: If the definite integral from 0 to 2 of (e^(x^2)) is first approximated by using two inscribed rectangles of equal width and then approximated by using the trapezoidal rule with n=2, the difference between the two approximations is what?

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  1. x f(x)
    0 1
    1 e
    2 e^4

    So, if there are 2 rectangles of width 1, then the area, using left-sides is

    1*1 + 1*e = e+1 = 3.718

    using right-sides, it's

    1*e + 1*e^4 = 57.316

    Using the trapezoidal rule, we have

    1(1+e)/2 + 1(e+e^4)/2 = 30.517

    Kind of a coarse approximation.

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  2. Thank you!

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