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When we use the midpoint rule or trapezoid rule we can actually calculate the maximum error in the calculation to get an idea how much we are off of the actual value.
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To calculate the error when using the trapezoid rule, we use the following formula: where K is the maximum value of |f’’(x)| on the interval.
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To calculate the error when using the midpoint rule, we use the following formula: where K is the maximum value of |f’’(x)| on the interval.
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Use n=6 to approximate the area under the curve on the interval [0, 1] using the midpoint rule.
![ Use n=6 to approximate the area under the curve on the interval [0, 1] using the midpoint rule.](http://images.slideplayer.com./25/8250822/slides/slide_5.jpg " Use n=6 to approximate the area under the curve on the interval [0, 1] using the midpoint rule.")
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Calculate the error from the previous problem.
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What would you make n t0 ensure that you are within.0001 of the actual area
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Use n=6 to approximate the area under the curve on the interval [0, 1] using the trapezoid rule.
![ Use n=6 to approximate the area under the curve on the interval [0, 1] using the trapezoid rule.](http://images.slideplayer.com./25/8250822/slides/slide_8.jpg " Use n=6 to approximate the area under the curve on the interval [0, 1] using the trapezoid rule.")
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Calculate the error from the previous problem.
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What would you make n to ensure that you are within.0001 of the actual area?
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Approximate the area under the curve on the interval [0, 4] using both the midpoint and trapezoid rules. Find the error of both. N=6
![Approximate the area under the curve on the interval [0, 4] using both the midpoint and trapezoid rules.](http://images.slideplayer.com./25/8250822/slides/slide_11.jpg "Find the error of both. N=6.")
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