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Ephilo
HELP PLEASE ...Find the upper and lower sums of f(x) = -2x + 4 on the interval [0, 2] partitioned into four subintervals of equal length.
a= 0 b=2 n= 4 dx = (b-a)/n= (2-0)/4=1/2 xi = a + idx = i/2 \[\sum_{i=1}^{n}f(x i)dx\] \[\sum_{i=1}^{4}(-2(i/2)+x ) \times 1/2\] develop \[\sum_{i=1}^{4}-i/2 +\sum_{i=1}^{4}2 \] use formulas for i and c sums \[-1/2\sum_{i=1}^{4}i+\sum_{i=1}^{4}2= -1/2 \times \frac{ n(n+1) }{ 2 } + 2n = -1/2 \times \frac{ 4(4+1) }{ 2 } = -5\]