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Definite Integrals

General Riemann Sums Examples

Example 1

Let f (x) = x3. Use a left-hand sum with 3 sub-intervals to estimate . Is your answer an over- or under-estimate?

Example 2

Use a midpoint sum with 2 sub-intervals to estimate . Is your answer an over-estimate or an under-estimate?

Example 3

Use LHS(3) to approximate . Is your answer an over- or under-estimate?

Example 4

Use TRAP(1) to estimate .

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