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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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