Notes: Evaluate The Upper And Lower Sums For F(x) = 2 + Sin X, 0 ‰¤ X ‰¤ Ï€, With N = 2, 4, And 8. Illustrate With Diagrams Like The Figure Shown Below. (round Your Answers To Two Decimal Places.)

Saturday, 4 October 2014

Evaluate The Upper And Lower Sums For F(x) = 2 + Sin X, 0 ‰¤ X ‰¤ Ï€, With N = 2, 4, And 8. Illustrate With Diagrams Like The Figure Shown Below. (round Your Answers To Two Decimal Places.)

The upper sum
of the integral

$\displaystyle{\int_{{a}}^{{b}}}{f{{\left({t}\right)}}}{\left.{d}{t}\right.}$

$U=sum_{i=0}^{n-1} f(x^+) Delta x$ where $\displaystyle\delta{x}=\frac{{{b}-{a}}}{{n}}$ , $\displaystyle{f{{\left({{x}}^{+}\right)}}}=\max{\left({f}\right)}$ on the
interval $[x_i,x_{i+1}]$ and $\displaystyle{x}_{{i}}={a}+{i}\delta{x}$

The lower sum is

$L=sum_{i=0}^{n-1} f(x^-) Delta x$ where $\displaystyle{f{{\left({{x}}^{{-}}\right)}}}=\min{\left({f}\right)}$ on the same
interval

Since $\displaystyle{f{{\left({x}\right)}}}={2}+{\sin{{x}}}$ , and the bounds on the...

Notes

Saturday, 4 October 2014

Evaluate The Upper And Lower Sums For F(x) = 2 + Sin X, 0 ‰¤ X ‰¤ Ï€, With N = 2, 4, And 8. Illustrate With Diagrams Like The Figure Shown Below. (round Your Answers To Two Decimal Places.)

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