This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1 4.8 Antiderivatives A physicist, who knows the position x ( t ) of a particle, can easily calculate the velocity of it by differentiation. Assume now, that a different physicist can only measure the velocity v ( t ), but he wishes to know both x ( t ) and v ( t ). Is it possible to find x ( t ) given its derivative? Definition A function is called an of f ( x ) on an interval I if: for all x in I . In other words, F is an antiderivative of f if the derivative of F is f . Example 1 Find an antiderivative of f ( x ) = 2 x Theorem If F ( x ) is an antiderivative of f ( x ) on an interval I then the of f on I is where is an constant. The table of antiderivatives of most common elementary functions is given in Table 4.2 on page 297 in University Calculus. Example 2 Find an antiderivative of f ( t ) = 1 t 4 = t 4 2 Example 3 Find an antiderivative of h ( s ) = sin(2 s ) Example 4 Find an antiderivative of f ( x ) = x n and g ( x ) = 4 x 2 / 7 Initial Value Problems (IVP) Typical IVP asks you to find a function...
View Full
Document
 Fall '08
 LLHanks
 Antiderivatives, Derivative

Click to edit the document details