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.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

step-by-step explanation: