Class notes
Class notes 201-NYB-05
- Course
- Institution
These notes cover all topics seen in Calculus 2
[Show more]
Seller
Follow
clarahamilton
Content preview
Antiderivativesdefinition : F(x) is an antiderivative of f(x) on an interva
on I
F(x) (f(x) differenciation f(x) is the derivative
f (x) (F(x) antidifferenciation
General antiderivative
taken from mean value theorem (f'(x) g'(x) , then f(x) = g(x)
i
=
If f(x) & g(x) are both antiderivatives of a function h(x
Basic antiderivative rules
- if
you are asked to evaluate (f(x)dx ,
you are asked to
> f(x) = F'(x) for some function F(x)
· The basic antiderivative rules are the basic derivative rule
Indefinite
Integral
f f(x)dx =
F(x) + C
<
any two antiderivatives of a same function m
constant
Substitution rule
< chain rule backwards :
(f(g(x)) .
g'(x)dx =
f f(u)du , let u
< visual v=g(x) is usually inside something (ex expo
cues : :
<
U'=g'(X) is being multiplied by dx (on the same level
<sometimes work is necessary to find g(x) (ex laws of ex :
fractions polynomial long division etc
, h ,
recall :
Ix + a2dx =
&arctan(a) + C
Si 1ax=-02
arcsin( *) + C
Integration by parts :
product rule backwards
recall :
[f(x)g(x)) =
f'(x)g(x) +
g'(x) f(x)
So :
((f(x)g(x()'dx f(f'(x)g(x) g'(x)f(x))dx = +
<
f(x)g(x) f f'(x)g(x)dx (g'(x) f(x)dx
= +
,
The benefits of buying summaries with Stuvia:
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
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
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 clarahamilton. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $10.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
56326 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now