Evaluate The Upper And Lower Sums For F(x) = 2 + Sin X, 0 ≤ X ≤ π, With N = 2, 4, And 8. Illustrate With Diagrams Like The Figure Shown Below. (round Your Answers To Two Decimal Places.)
Evaluate the upper and lower sums for f(x) = 2 + sin x, 0 ≤ x ≤ π, with n = 4 , 8?
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The upper sum of the integral
`int_a^b f(t)dt`
is
`U=sum_{i=0}^{n-1} f(x^+) Delta x` where `Delta x = {b-a}/n` , `f(x^+)=max(f)` on the interval `[x_i,x_{i+1}]` and `x_i=a+i Delta x`
The lower sum is
`L=sum_{i=0}^{n-1} f(x^-) Delta x` where `f(x^-)=min(f)` on the same interval
Since `f(x)=2+sin x` , and the bounds on the...
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