Integration by Parts



Calculus BC: Q203 – Lesson 1: Integration by Parts

Up to this stage we have been unable to evaluate integrals such as the following:

[pic]

The next formula will enable us to evaluate not only these, but also many other types of integrals.

If [pic]and [pic]and if [pic]and [pic]are continuous, then [pic]

Proof:

Example 1: Evaluate [pic]

Example 2: Evaluate [pic]

Example 3: Evaluate [pic]

Example 4: Evaluate [pic]

Example 5: Evaluate [pic]

Evaluate [pic]

Tabular integration

(Q203 – Lesson 1) Integration by Parts Supplement Homework

Evaluate each integral.

1. [pic]

2. [pic]

3. [pic]

4. [pic]

5. [pic]

6. [pic]

7. [pic]

8. [pic]

Calculus BC: Q203 – Lesson 2 (Section 6.5 Notes): Integration by Partial Fractions

Calculus BC: Q203 – Lesson 2 (Supplemental Notes): Integration by Trigonometric Substitutions

|Expression in Integrand |Trigonometric Substitution |

|[pic] |[pic] |

|[pic] |[pic] |

|[pic] |[pic] |

Example 1: Evaluate [pic]

Example 2: Evaluate [pic]

Example 3: Evaluate[pic]

HW: SUPPLEMENT – Evaluate Each

#42. [pic]

#35. [pic]

#37. [pic]

#39. [pic]

MISC. EXTRA: [pic]

Finish using [pic] substitution.

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