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User Pbeta
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The Rieman sum is used as an approximation when performing integration. It attempts to find an approximate value for the area under the curve.

A left Riemann sum uses rectangles whose top-left vertices are on the curve. A right Riemann sum uses rectangles whose top-right vertices are on the curve. We are therefore given a right-hand Rieman sum.

To calculate the Rieman sum we first note that there are eight rectangles therefore eight intervals.

The base of each rectangle = 0.5


\begin{gathered} We\text{ know that f\lparen x\rparen = }(x^2)/(8) \\ Area\text{ = 0.5\lparen1.531 + 2+ 2.531 +3.125 + 3.781+4.5 +5.281+6.125\rparen} \\ \text{ = 14.437} \\ \end{gathered}

As this is a righ-hand Riemann sum and we can see that the rectangles reach above the cure, we can conclude that it is an over-estimation.

User Sino
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