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AP Calculus BC October 11, 2016.

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Presentation on theme: "AP Calculus BC October 11, 2016."โ€” Presentation transcript:

1 AP Calculus BC October 11, 2016

2 Entry Task ๐‘ฅ+7 ๐‘‘๐‘ฅ ๐‘ฅ+6 ๐‘ฅ ๐‘‘๐‘ฅ sec ๐‘ฆ tan ๐‘ฆ โˆ’ sec ๐‘ฆ ๐‘‘๐‘ฆ
Find the indefinite integral: ๐‘ฅ+7 ๐‘‘๐‘ฅ ๐‘ฅ+6 ๐‘ฅ ๐‘‘๐‘ฅ sec ๐‘ฆ tan ๐‘ฆ โˆ’ sec ๐‘ฆ ๐‘‘๐‘ฆ

3 Learning Targets I understand the definition of a Riemann Sum
I understand how to evaluate a definite integral using limits and properties of definite integrals I can evaluate definite integrals.

4 Evaluating Definite Integrals
Find the integral: โˆ’2 1 2๐‘ฅ ๐‘‘๐‘ฅ Area under the curve

5 Area of common geometric figures
1 3 4 ๐‘‘๐‘ฅ 0 3 ๐‘ฅ+2 ๐‘‘๐‘ฅ โˆ’ โˆ’ ๐‘ฅ 2 ๐‘‘๐‘ฅ

6 Properties of Definite Integrals
๐œ‹ ๐œ‹ sin ๐‘ฅ ๐‘‘๐‘ฅ = ? 3 0 ๐‘ฅ+2 ๐‘‘๐‘ฅ= ? โˆ’ 0 3 ๐‘ฅ+2 ๐‘‘๐‘ฅ = ? โˆ’2 0 ๐‘ฅ 2 ๐‘‘๐‘ฅ ๐‘ฅ 2 ๐‘‘๐‘ฅ = ? โˆ’2 2 ๐‘ฅ 2 ๐‘‘๐‘ฅ= ?

7 Properties of Definite integrals
2 4 4 ๐‘ฅ 2 ๐‘‘๐‘ฅ = ? ๐‘ฅ 2 ๐‘‘๐‘ฅ = ? 1 3 โˆ’ ๐‘ฅ 2 +4๐‘ฅ โˆ’3 ๐‘‘๐‘ฅ = ?

8 Homework #17 ยง4.3 #44, 47, 48, 52

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