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AP Calculus Mrs. Mongold
Lesson 2: Area Take 2 AP Calculus Mrs. Mongold
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Note LRAM and RRAM are different then upper and lower sums!!!
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When n=4 ,โ๐ฅ= ๐ 4 0 ๐ ๐ ๐๐๐ฅ๐๐ฅโ ๐ 8 ๐ ๐๐0+2๐ ๐๐ ๐ 4 +2๐ ๐๐ ๐ 2 +2๐ ๐๐ 3๐ 4 +๐ ๐๐๐ 0 ๐ ๐ ๐๐๐ฅ๐๐ฅโ ๐ 8 ๐ ๐๐0+2๐ ๐๐ ๐ 4 +2๐ ๐๐ ๐ 2 +2๐ ๐๐ 3๐ 4 +๐ ๐๐๐
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When n=4 ,โ๐ฅ= ๐ 4 0 ๐ ๐ ๐๐๐ฅ๐๐ฅโ ๐ 8 ๐ ๐๐0+2๐ ๐๐ ๐ 4 +2๐ ๐๐ ๐ 2 +2๐ ๐๐ 3๐ 4 +๐ ๐๐๐ 0 ๐ ๐ ๐๐๐ฅ๐๐ฅโ ๐ 8 ๐ ๐๐0+2๐ ๐๐ ๐ 4 +2๐ ๐๐ ๐ 2 +2๐ ๐๐ 3๐ 4 +๐ ๐๐๐ โ ๐
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When n=4 ,โ๐ฅ= ๐ 4 0 ๐ ๐ ๐๐๐ฅ๐๐ฅโ ๐ 8 ๐ ๐๐0+2๐ ๐๐ ๐ 4 +2๐ ๐๐ ๐ 2 +2๐ ๐๐ 3๐ 4 +๐ ๐๐๐ 0 ๐ ๐ ๐๐๐ฅ๐๐ฅโ ๐ 8 ๐ ๐๐0+2๐ ๐๐ ๐ 4 +2๐ ๐๐ ๐ 2 +2๐ ๐๐ 3๐ 4 +๐ ๐๐๐ โ ๐ โ1.896
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When n = 8, โ๐ฅ= ๐ 8 0 ๐ ๐ ๐๐๐ฅ๐๐ฅโ ๐ 16 ( ๐ ๐๐0+2๐ ๐๐ ๐ 8 +2๐ ๐๐ ๐ 4 +2๐ ๐๐ 3๐ 8 +2๐ ๐๐ ๐ 2 +2๐ ๐๐ 5๐ 8 +2๐ ๐๐ 3๐ 4 +2๐ ๐๐ 7๐ 8 +๐ ๐๐๐)
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When n = 8, โ๐ฅ= ๐ 8 0 ๐ ๐ ๐๐๐ฅ๐๐ฅโ ๐ 16 ( ๐ ๐๐0+2๐ ๐๐ ๐ 8 +2๐ ๐๐ ๐ 4 +2๐ ๐๐ 3๐ 8 +2๐ ๐๐ ๐ 2 +2๐ ๐๐ 5๐ 8 +2๐ ๐๐ 3๐ 4 +2๐ ๐๐ 7๐ 8 +๐ ๐๐๐) โ ๐ ๐ ๐๐ ๐ 8 +4๐ ๐๐ 3๐ 8
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When n = 8, โ๐ฅ= ๐ 8 0 ๐ ๐ ๐๐๐ฅ๐๐ฅโ ๐ 16 ( ๐ ๐๐0+2๐ ๐๐ ๐ 8 +2๐ ๐๐ ๐ 4 +2๐ ๐๐ 3๐ 8 +2๐ ๐๐ ๐ 2 +2๐ ๐๐ 5๐ 8 +2๐ ๐๐ 3๐ 4 +2๐ ๐๐ 7๐ 8 +๐ ๐๐๐) โ ๐ ๐ ๐๐ ๐ 8 +4๐ ๐๐ 3๐ 8 โ1.974
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Evaluate Using Antiderivative
0 ๐ ๐ ๐๐๐ฅ๐๐ฅ
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Evaluate Using Antiderivative
0 ๐ ๐ ๐๐๐ฅ๐๐ฅ - (๐๐๐ ๐โ๐๐๐ 0)
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Evaluate Using Antiderivative
0 ๐ ๐ ๐๐๐ฅ๐๐ฅ - (๐๐๐ ๐โ๐๐๐ 0) A=2
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Verify your approximation with your calculator๏
Graph f(x) 2nd Calc # ๐ ๐ฅ ๐๐ฅ Enter upper and lower bounds
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