Loading in 5 sec....

More U-Substitution: The “Double-U” Substitution with ArcTan(u)PowerPoint Presentation

More U-Substitution: The “Double-U” Substitution with ArcTan(u)

- 197 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' More U-Substitution: The “Double-U” Substitution with ArcTan(u)' - holleb

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

Techniques of Integration so far…

- Use Graph & Area ( )
- Use Basic Integral Formulas
- Simplify if possible (multiply out, separate fractions…)
- Use U-Substitution…..

Substitution Rule for Indefinite Integrals

- If u = g(x) is a differentiable function whose range is an interval I and f is continuous on I, then

Substitution Rule for Definite Integrals

- If g’(x) is continuous on [a,b] and f is continuous on the range of u = g(x), then

Compare the two Integrals:

Extra “x”

Notice that the extra ‘x’ is the same power as in the substitution:

Extra “x”

Compare:

Still have an extra “x” that can’t be related to the substitution.

U-substitution cannot be used for this integral

Evaluate:

Returning to the original variable “t”:

Evaluate:

Returning to the original variable “t”:

Evaluate:

Returning to the original variable “t”:

Use:

It’s necessary to know both forms:

t2 - 2t +26 and 25 + (t-1)2

t2 - 2t +26 = (t2 - 2t + 1) + 25 = (t-1)2+ 25

Completing the Square:

- Comes from

Use to solve:

- How do you know WHEN to complete the square?

Ans: The equation x2 + x + 3 has NO REAL ROOTS (Check b2 - 4ac)

If the equation has real roots, it can be factored and later we will use Partial Fractions to integrate.

Evaluate: solve:

Try these: solve:

Download Presentation

Connecting to Server..