Limits of Integration
Definition
The limits of integration are the values that determine the range over which an integral is evaluated. They specify the starting and ending points on the x-axis for finding the area or calculating other quantities using integration.
Analogy
Think of limits of integration as the boundaries of a playground. Just like you can only play within the designated area, when evaluating an integral, you can only calculate within the specified limits.
Related terms
Definite Integral: A definite integral is used to find the exact value of an area under a curve or to calculate other quantities. It involves integrating a function between specific limits.
Indefinite Integral: An indefinite integral represents a family of functions that differ by a constant. It does not have specific limits and is often used to find antiderivatives.
Riemann Sum: A Riemann sum is an approximation method for finding areas under curves by dividing them into smaller rectangles. It becomes more accurate as these rectangles become narrower.
"Limits of Integration" appears in:
Study guides (4)
Additional resources (1)
Practice Questions (6)
Which property of definite integrals states that the integral of a function is unchanged when its limits of integration are reversed?
What are the limits of integration used for in finding the volume of a solid with cross sections?
When revolving a region bounded by the graph of a function f(x) and the x-axis around the y-axis, what should be the limits of integration in the volume formula?
Which limits of integration should be used when finding the volume of a solid of revolution?
What determines the appropriate formula for the area of each disc and the limits of integration when revolving a solid around an axis?
What does the choice of limits of integration represent when calculating the volume of a solid of revolution?
Are you a college student?
Study guides for the entire semester
200k practice questions
Glossary of 50k key terms - memorize important vocab
Resources
© 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.