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AP Calculus BC Monday, 18 November 2013 OBJECTIVE TSW use integration by subsitution. ASSIGNMENT DUE –Sec. 4.1 wire basket Tests are graded. Look on line for your score. –Due to time constraints, we will not go over them in class. –If you would like to look at your test, arrange to come in during lunch, before school, or after school. The test for indefinite integration has been pushed back to this Friday, 22 November 2013.

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Sec. 4.5: Integration by Substitution

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Rewrite the integral:

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Sec. 4.5: Integration by Substitution u = 7x du = 7 dx

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Sec. 4.5: Integration by Substitution u = x 2 – 4 du = 2x dx 1/2 du = x dx

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Sec. 4.5: Integration by Substitution u = sin 3x du = (cos 3x) 3 dx 1/3 du = cos 3x dx

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Sec. 4.5: Integration by Substitution u = 5x + 3 du = 5 dx 1/5 du = dx

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Sec. 4.5: Integration by Substitution Rearranging u u = x + 3 du = dx u – 3 = x

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Sec. 4.5: Integration by Substitution u = 2x – 1 du = 2 dx u + 1 = 2x 1/2 du = dx (u + 1) / 2 = x

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Integration by Substitution Lesson 5.5. Substitution with Indefinite Integration This is the “backwards” version of the chain rule Recall … Then …

Integration by Substitution Lesson 5.5. Substitution with Indefinite Integration This is the “backwards” version of the chain rule Recall … Then …

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