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 a calculator. (round your answers to the nearest whole number.) y = 1 5 x5, 0 ≤ x ≤ 5

The area of the surface is given exactly by the integral,

We have

so the area is

We split up the domain of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [4, 9/2], [9/2, 5]

where the left and right endpoints for the -th subinterval are, respectively,

with midpoint

with .

Over each subinterval, we interpolate with the quadratic polynomial,

Then

It turns out that the latter integral reduces significantly to

which is about 651.918, so that the area is approximately .

Compare this to actual value of the integral, which is closer to 1967.

8y^50

step-by-step explanation: