SOLUTION: Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = -x^3 and y = -x.

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Question 1119908: Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = -x^3 and y = -x.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You didn't give limits so I'll make my own.
You can modify the solution as needed.
.
So find the area between x=-1 and x=0.
The four regions are from
x=-1 to x=-0.75
x%5BM1%5D=-0.875
x=-0.75 to x=-0.5
x%5BM2%5D=-0.625
x=-0.5 to x=-0.25
x%5BM3%5D=-0.375
x=-0.25 to x=0
x%5BM4%5D=-0.125
Find the difference of the functions at the midpoints,
D=-x-%28-x%5E3%29=x%5E3-x
So,
D%5B1%5D=%28-0.875%29%5E3%2B0.875=0.205078
D%5B2%5D=%28-0.625%29%5E3%2B0.625=0.380859
D%5B3%5D=%28-0.375%29%5E3%2B0.375=0.322266
D%5B4%5D=%28-0.125%29%5E3%2B0.125=0.123047
Sum the differences and multiply by the step in x 0.25,
A%5B4%5D=%280.205078%2B0.380859%2B0.322266%2B0.123047%290.25
A%5B4%5D=1.03125%280.25%29
A%5B4%5D=0.257