Calculus I - PowerPoint PPT Presentation

PPT – Calculus I PowerPoint presentation | free to view - id: e222d-MWMxN

The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
Title:

Calculus I

Description:

indefinite integral of f, and we introduce the. notation ... NOTE to find the indefinite integral is the. same as to find the most general antiderivative ... – PowerPoint PPT presentation

Number of Views:104
Avg rating:3.0/5.0
Slides: 10
Provided by: moni64
Category:
Transcript and Presenter's Notes

Title: Calculus I

1
Calculus I
• AntiDerivatives

2
AntiDerivatives
• Def Let f be a continuous function,
• we say that F is an antiderivative of f
• on some interval I, provided that Ff on I.
• Note that f has infinitely many antiderivatives.
• To express this we will say that given a
continuous
• function f on I, we say that the most general
antiderivatives of
• function f, is F c, where c is an arbitrary
constant and
• F f.

3
AntiDerivative
• How do we do this? We read the
• derivative tables backwords ?!
• Example Given f(x) cos x, we can say
• the most general antiderivative of f is
• F(x) sin x C.

4
AntiDerivative
• Example Find the most general
• antiderivative of the following
• functions
• 1) f(x) 1
• 2) g(x) x
• 3) h(x) sec x tan x
• 4) k(x) ex

5
AntiDerivative
• Applications?
• Lets suppose that f(x) sec2 x x
• and suppose f(0) -3.

6
AntiDerivative
• Lets suppose that f(x) cos x 2ex 3x 5
• and suppose f(0) -3 and f(0) 2.

7
AntiDerivative
• More formally, the most general antiderivative
• of a continuous function f is defined to be the
• indefinite integral of f, and we introduce the
• notation
• Example

8
AntiDerivative
• Rules of Integration
• NOTE to find the indefinite integral is the
• same as to find the most general antiderivative
• of a function. Thus, we read the derivative
• Tables from right to left. In addition, we have