study guides for every class

that actually explain what's on your next test

Integrally-defined Function

from class:

AP Calculus AB/BC

Definition

An integrally-defined function is a function whose values are obtained by integrating another function over an interval. It represents an accumulation process where we add up infinitesimally small pieces (represented by dx) of another function.

"Integrally-defined Function" also found in:

Practice Questions (7)

The derivative of an integrally-defined function $h(x)$ is given by $f(x)$, in other words h(x) = ∫f(x) dx. If $f(x)$ is positive on an interval $(a, b)$, what can be said about the behavior of $h(x)$ on that interval?
What is an integrally-defined function?
If the graph of the first derivative $f(x)$ of an integrally-defined function $h(x)$ is below the x-axis on an interval $(e, f)$, what can be concluded about the behavior of $h(x)$ on that interval?
If the graph of the first derivative $f(x)$ of an integrally-defined function $h(x)$ is increasing on the interval $(g, h)$, what can be said about the behavior of $h(x)$ on that interval?
If the graph of the first derivative $g(x)$ of an integrally-defined function $h(x)$ is decreasing on the interval $(i, j)$, what can be said about the behavior of $h(x)$ on that interval?
If the graph of the first derivative $f(x)$ of an integrally-defined function $h(x)$ changes from negative to positive at $x = k$, what can be concluded about $h(x)$ at $x = k$?
If the graph of the first derivative $f(x)$ of an integrally-defined function $h(x)$ changes from positive to negative at $x = l$, what can be concluded about $h(x)$ at $x = l$?

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

Back

Practice QuizGlossary

Practice Quiz Guides

study guides for every class

that actually explain what's on your next test

Integrally-defined Function

from class:

AP Calculus AB/BC

Definition

"Integrally-defined Function" also found in:

Practice Questions (7)

© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

Back

Next

study guides for every class

that actually explain what's on your next test

Integrally-defined Function

from class:

AP Calculus AB/BC

Definition

Related terms

"Integrally-defined Function" also found in:

Practice Questions (7)

© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

Back

Next