100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Summary Partial Fraction Decomposition | Calculus II Notes $8.29   Add to cart

Summary

Summary Partial Fraction Decomposition | Calculus II Notes

 3 views  0 purchase
  • Course
  • Institution

Details how to integrate some rational functions using partial decomposition. Includes broken down and step by step instructions to solve examples for linear factor cases and irreducible quadratic factor in the denominator.

Preview 1 out of 4  pages

  • July 16, 2023
  • 4
  • 2022/2023
  • Summary
avatar-seller
1.10 Partial Fraction Decomposition
for integrating some rational functions


First:if the degree of the numerator is greater than the degree of the denominator, do long division



eg.( xs,2432dx
x3 -

3x quotient
x
2
3x5
+ -
6x + 2 divisor numerator
u
=(Xs 3x") +




x(x3) -

343 -

6x 2 +




-- (3x 9x) -




x(3x) 3x+2 divisor, stop
when the
degree of the remainder is less than the long division

numerator quotient
- remainder
+




divisor divisor



x5 6x 2 (x3 3x)
3
- +
- +




2*3*
=




23
x +
3
e
S x5 -6x 2dx f(x3 x
2
+

3
+
=
-
3x)dx 3x
+



S 2
x
+




3
+




=** 2
3)Y
+
+




un
ux+
=
3
Y5
u =




du 2XdX
=




du
dx
=




I(=en(u) 3( - arctan(u)


arctan(*)
=** x en(x+3) +o
- + +




3



you only need to look at
see
when
degreep(x) degree q(x)
"Partial fractions"


eg. S, dx factor the denominator ( (x2-1) (x 1)(x 1) =
- +




write
integral as sum offrations
1 = A B
+



-
x 1 x 1 +
x -
1


A(X-1) B(x+1)
= +




x2 -
1

solve for numerators
a) equatenumerators after combining fractions
1 A(x-1) B(x+ 1)
= +



expand, collectlike terms, factor out common is
0x + 1 (A B)x=
+
(
+ -

A B)+
-




Ax Bx +
0x
=




-
A B
+
1
=

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller dazyskiies. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $8.29. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

80467 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$8.29
  • (0)
  Add to cart