{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture29

# lecture29 - Math 121 Lecture 29 Derivatives Definition...

This preview shows pages 1–7. Sign up to view the full content.

Math 121 Lecture 29 Derivatives: Definition. Techniques. Applications.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
! Antidifferentiation ! Areas and Riemann Sums ! Definite Integrals and the Fundamental Theorem ! Areas in the xy -Plane ! Applications of the Definite Integral § 6.1 Antidifferentiation
! Antidifferentiation ! Finding Antiderivatives ! Theorems of Antidifferentiation ! The Indefinite Integral ! Rules of Integration ! Antiderivatives in Application Definition Example Antidifferentiation : The process of determining f ( x ) given f ! ( x ) If , then

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Find all antiderivatives of the given function. The derivative of x 9 is exactly 9 x 8 . Therefore, x 9 is an antiderivative of 9 x 8 . So is x 9 + 5 and x 9 -17.2. It turns out that all antiderivatives of f ( x ) are of the form x 9 + C (where C is any constant) as we will see next.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Determine the following. Using the rules of indefinite integrals, we have Find the function f ( x ) for which and f (1) = 3. The unknown function f ( x ) is an antiderivative of . One antiderivative is . Therefore, by Theorem I, Now, we want the function f ( x ) for which f (1) = 3. So, we must use that information in our antiderivative to determine C . This is done below.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}