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.
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.
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Study guides (4)
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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?
