Status: Tags: Links: IBP Special Cases
Polynomial + Trig or Exponential Special Case (Table Method)
Principles
- Used to evaluate Integration By Parts (IBP) polynomials where
u = polynomialanddv = trig or exponential - Set up the special case table and multiply the item in the u column by the dv to the bottom right of it
- Alternate between positive and negative
- Keep adding into equation before for values where the derivative of u > 0
Table
For $\int{x^2e^{2x}dx}$
| u (d) | dv (anti-d) |
|---|---|
| $x^2$ | $e^{2x}$ |
| 2x | $\frac12e^{2x}$ |
| 2 | $\frac14e^{2x}$ |
| 0 | $\frac18e^{2x}$ |
Anki
START Cloze The {Table Method::method} is used for cases where u and dv are {polynomial and trig/exponential::type of thing}. The grouped terms should alternate between {positive and negative::sign changes} Back: DECK: IntegralCalculus Tags: IBP
END
Practice
References: