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?

Answer 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.

Answer 2

Thank you!

Answer 3

Steve's answer is unfortunately incorrect. 30.517 was wrong when picked.

Answer 4

The answer is 26.80

Answer 5

Steve is correct. He gave us both the LH & RH approximations as well as the trapezoid approximation

You just needed to subtract Trapezoid & the LH which gives 30.517-3.718 = 26.80