The midpoint approximation of the area under the curve f(x) = 2x(x-4)(x-8) over the interval [0, 4] with 4 subintervals is 132.
How to calculate the midpoint?
The value of f(1/2) will be:
= 2(1/2)(1/2 - 4)(1/2 - 8)
= 105/4
The value of f(3/2) will be:
= 2(3/2)(3/2 - 4)(3/2 - 8)
= 195/4
The value of f(5/2) will be:
= 2(5/2)(5/2 - 4)(5/2 - 8)
= 165/4
The value of f(7/2) will be:
= 2(7/2)(7/2 - 4(7/2 - 8)
= 63/4
Therefore, the midpoint approximation will be:
= 1/4(105 + 195 + 165 + 63)
= 132
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