Use simpson's rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. compare your answer with the value of the integral produced by your calculator. (round your answer to six decimal places.) y = e−x2, 0 ≤ x ≤ 2

Split up the integration interval [0, 2] into 10 subintervals:

[0, 1/5], [1/5, 2/5], [2/5, 3/5], ..., [9/5, 2]

The left and right endpoints of the -th subinterval are, respectively,

with midpoints

for .

Simpson's rule approximates the definite integral

by interpolating the integrand, , over each subinterval with a quadratic polynomial, , such that

You would end up with a value of about 6.497681. Compare to the actual value of the integral, which is closer to 6.497684.

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step-by-step explanation: