Double integrals over General Regions. (HELP PLEASE )

In summary, the conversation discusses using a computer algebra system to find the exact volume of a solid under the surface z = x^3 * y^4 + xy^2 and above a region bounded by the curves y = x^3 - x and y = x^2 + x for x >= 0. The user asks for assistance in using the computer algebra system and provides assumptions for the limits of integration. They also inquire about the need for a TI-89 calculator.
  • #1
afcwestwarrior
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Double integrals over General Regions. (HELP PLEASE !)

Use a computer algebra system to find the exact volume of the solid.

Under the surface z = x^3 * y^4 + xy^2

and above the region bounded by the curves y = x^3 - x and y = x^2 + x for x >= 0



How do I use a computer algebra system to find the volume.
 
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  • #2


Do you want the algorithm to find the limits for you then solve it? Or do you require the user to know the limits etc...

We need some assumptions about your program.
 
  • #3


The limits for X is 0 to -1 and for Y it's -.25 to .4

Do I need a TI-89 to do this problem.
 
  • #4


First, simple solve the integral by hand to get a check value against the computer system.
 

1. What is a double integral?

A double integral is a type of integral that allows you to calculate the volume under a three-dimensional surface. It involves integrating a function over a two-dimensional region.

2. How is a double integral different from a single integral?

A single integral involves integrating a function over a one-dimensional interval, while a double integral involves integrating a function over a two-dimensional region. This allows you to calculate the volume under a three-dimensional surface instead of just the area under a curve.

3. What is a general region?

A general region is any two-dimensional shape, such as a rectangle, triangle, or circle, that can be described using equations or inequalities. It can be bounded by curves or lines, and may also have holes or disjointed regions.

4. How do you find the bounds for a double integral over a general region?

To find the bounds for a double integral over a general region, you need to first identify the equations or inequalities that define the boundaries of the region. Then, you can use these equations to determine the limits of integration for each variable.

5. What are some applications of double integrals over general regions?

Double integrals over general regions are commonly used in physics, engineering, and economics to calculate the volume under a three-dimensional surface. They are also useful for finding the mass, center of mass, and moments of inertia of an object. In addition, they can be used to calculate probabilities in statistics and to solve differential equations in mathematics.

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