Mathematics, 16.10.2019 20:00 alexis539
Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for the integral from 0 to 2 of x squared, dx .
Answers: 1
![[0,2]=\left[0,\dfrac12\right]\cup\left[\dfrac12,1\right]\cup\left[1,\dfrac32\right]\cup\left[\dfrac32,2\right]](/tpl/images/0326/0220/65114.png)
. The area of the trapezoid constructed on each subinterval is 
, i.e. the average of the values of 
at both endpoints of the subinterval times 1/2 over each subinterval ![[x_i,x_{i+1}]](/tpl/images/0326/0220/e9a74.png)
.
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Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower...
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