# Calculus

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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