Question

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.

Answer 1

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
\[-1/2\sum_{i=1}^{4}i+\sum_{i=1}^{4}2= -1/2 \times \frac{ n(n+1) }{ 2 } + 2n = -1/2 \times \frac{ 4(4+1) }{ 2 } = -5\]

Answer 2

thanks !!(: