1. 8.2 Integration By Parts Badlands, South Dakota
Greg Kelly, Hanford High School, Richland, Washington
Photo by Vickie Kelly, 1993

2. Objectives Find the antiderivative using integration by parts.
Use a tabular method to perform integration by parts.

3. Graphing Calculator Activity:
Graph and find the area bounded by
and
Window: xmin= ymin=-1.2
xmax=1.88 ymax=1.7
A valentine for your sweetie "pi".
fnInt(y2-y1,x,-1,1)
Shade(y1,y2) {Draw 7}

4. How do you integrate

5. 7.2 Integration By Parts Start with the product rule:
This is the Integration by Parts formula.

6. u differentiates to zero (usually).
dv is easy to integrate.
u differentiates to zero (usually).
The Integration by Parts formula is a “product rule” for integration.
Choose u in this order: LIATE
Logs, Inverse trig, Algebraic, Trig ,Exponential

7. LIATE

8. LIATE

9. Can't integrate arcsin!

10. Example 1:
LIATE
polynomial factor

11. This is still a product, so we need to use integration by parts again.

13. A Shortcut: Tabular Integration (Tic-Tac-Toe Method)
Tabular integration works for integrals of the form:
where:
Differentiates to zero in several steps.
Integrates repeatedly.

14. Compare this with the same problem done the other way:

15. Example 5:
This is easier and quicker to do with tabular integration!

17. Homework
Handout
#1-15 odd
21, 29, 31, 35 p