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Hence

Example 3 Evaluate the lower Riemann sum L ( P,f ) and the upper Riemann sum U ( P,f ) where P = { 0, 1/4, 1/3, 1/2, 3/4, 4/5, 1 } and f ( x ) = arctan x ,

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Example 1 (a) Estimate by the Midpoint, Trapezoid and Simpson's

Example 1 (a) Estimate by the Midpoint, Trapezoid and Simpson's Rules using the regular partition P of the interval [ 0,2 ] into 6 subintervals. (b) Find bounds on the errors of those approximations.

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Hence

Example 1 (a) Estimate by the Midpoint, Trapezoid and Simpson's