- #1
unscientific
- 1,734
- 13
Homework Statement
Homework Equations
The Attempt at a Solution
Are my limits of integration right?
Simple Volume Integral, limits of integration
- Thread starter unscientific
- Start date
In summary, a Simple Volume Integral is a mathematical technique used to calculate the volume of a three-dimensional object by dividing it into small, simple shapes and adding them together. The limits of integration for this type of integration are determined by the boundaries of the object being measured, which can be defined by equations or given in a problem statement. These limits can be negative if the boundaries extend into the negative direction of the coordinate axes. There is a difference between definite and indefinite limits of integration, with definite limits involving specific numerical values and indefinite limits involving variables or parameters. To calculate the volume, the cross-sectional area of the object is integrated with respect to the limits of integration, by multiplying it by an infinitesimal element of length and then integrating over the
Are my limits of integration right?
- #2
HallsofIvy
Science Advisor
Homework Helper
- 42,989
- 975
I would have done the integral in a different order. Obviously y will go from 0 to 2, z from 0 to 2, and, for each z, x from 0 to [itex]4- z^2[/itex].
- #3
unscientific
- 1,734
- 13
HallsofIvy said:
That should give the same answer, right?
1. What is a Simple Volume Integral?
A Simple Volume Integral is a mathematical technique used to calculate the volume of a three-dimensional object by dividing it into small, simple shapes and adding them together. It is a type of integration used in calculus.
2. How do you determine the limits of integration for a Simple Volume Integral?
The limits of integration for a Simple Volume Integral are determined by the boundaries of the object being measured. These boundaries can be defined by equations or given in a problem statement. It is important to correctly identify the limits in order to accurately calculate the volume.
3. Can the limits of integration for a Simple Volume Integral be negative?
Yes, the limits of integration for a Simple Volume Integral can be negative. This can occur when the boundaries of the object being measured extend into the negative direction of the coordinate axes.
4. What is the difference between definite and indefinite limits of integration for a Simple Volume Integral?
Definite limits of integration involve specific numerical values for the boundaries of the object being measured, whereas indefinite limits of integration involve variables or parameters. Definite limits are used to find an exact volume, while indefinite limits are used to find a general formula for the volume.
5. How is the volume calculated using a Simple Volume Integral?
The volume is calculated by integrating the function representing the cross-sectional area of the object with respect to the limits of integration. This involves multiplying the cross-sectional area by the infinitesimal element of length, such as dx, dy, or dz, and then integrating over the specified limits.
Similar threads
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help
-
Calculus and Beyond Homework Help