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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