riemann sum power point

8/6/2019 Riemann Sum Power Point

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Riemann Sums are used to approximate

the area between a curve and the x-axis over an

interval. Riemann sums divide the areas into

rectangles. By adding the areas of therectangles, one gets an approximation for the

area under the curve on the given interval.


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Usually Riemann sums will use equallysized partitions of the interval to make

calculations easier. By having bases of

equal length, the base can be factored out

when calculating the sum.


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Heres an example of how a Riemann Sum works:

).partitionsof#nwhere4,(npartitions4

usingcurveunder theareatheeapproximatsLet'

[1,3].intervalon the

x

1yfunctionheConsider t

!!

!

y=1/x


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ab !(

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y=1/x


6/18

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1x( 2x( 3x( 4x(

)1,1(

)0,1(

y=1/x


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9/18

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each rectangleusing the right

endpoint.


10/18

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it.gsimplifyin

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12/18

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getyoudoWhat

!!ZE !TGTE MTHEM T

.expressionor thislimtakeso

in inity,approachtointervalsonumberant theeemember,

n gp

meanthisdoesWhat3434

a:getyouid

3434bba

YOU NOW HAVE A FORMULA FOR THE AREA UNDER THE CURVEON ANY INTERVAL [a, b] FOR THE FUNCTION y = x3 x2.


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You now know how to use Riemann Sums!

The next step is to add a bit of Calculus to the mix.

Georg Friedrich Bernhard Riemann

Born: September 17, 1826Died: July 20, 1866

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