1. C.2.2 – Integration by Parts
Calculus - Santowski
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Calculus - Santowski

2. Lesson Objectives
Use the method of integration by parts to integrate simple power, exponential, and trigonometric functions both in a mathematical context and in a real world problem context
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Calculus - Santowski

3. (A) Product Rule
Recall that we can take the derivative of a product of functions using the product rule:
So we are now going to integrate this equation and see what emerges
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Calculus - Santowski

4. (B) Product Rule in Integral Form
We have the product rule as
And now we will integrate both sides:
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Calculus - Santowski

5. (B) Product Rule in Integral Form
We will make some substitutions to simplify this equation:
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Calculus - Santowski

6. (C) Integration by Parts Formula
So we have the formula
So what does it mean?
It seems that if we are trying to solve one integral
and we create a second integral !!!!
Our HOPE is that the second integral is easier to solve than the original integral
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Calculus - Santowski

7. (D) Examples
The easiest way to master the method is by practicing, so determine
We need to select a u and a dv
So we have a choice …..
Comment: Is the second integral any easier than the original???
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Calculus - Santowski

8. (D) Examples So let’s make the other choice as we determine
Checkpoint: Is our second integral any “easier” than our first one???
Now verify by differentiating the answer
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Calculus - Santowski

9. (E) Further Examples Integrate the following: 5/20/2018
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10. (E) Further Examples
For the following question, do it using the method requested. Reconcile your solution(s)
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Calculus - Santowski

11. (E) Further Examples These examples are slightly more challenging
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Calculus - Santowski

12. (F) Internet Links
Integration by Parts from Paul Dawkins, Lamar University
Integration by Parts from Visual Calculus
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Calculus - Santowski

13. (G) Homework Textbook, §8.1, p466-468; (1) Q3,5,7,9,11
(2) Q13-22 (mixed practice)
(3) Q35,37,39 (Word Problems)
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Calculus - Santowski