Calculating Volume Using Double Integrals: Finding the Boundaries and Limits

In summary, the conversation discusses finding the volume of three different solids bounded by two given surfaces, with specific boundaries on the sides. The speaker is seeking help in understanding how to approach this type of problem for an upcoming exam. They are advised to try solving the problems themselves as the best way to learn mathematics.
  • #1
rclakmal
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Homework Statement




given two surfaces S1={(x,y,z)|z=50-X^2} S2={(x,y,z)|z=9y^2+16} find the volume

1.V1 bounded above by S1 and below by S2 and on the sides by the vertical planes X=1 X=-1 Y=1 Y=-1

2 the solid V2 bounded above by S1 and below by S2 and on the sides by the vertical cylinder X^2+y^2=1

3.the solid V3 which is bounded above by the surface S1 below by S2

Homework Equations





The Attempt at a Solution



hey Please give me a help because i don't have much time !exam is today and want to understand these kind of questions !it will be nice if u can give me the steps to solve this kind of problem rather that giving answers to this questions!
 
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  • #2
The exam is today and you have no idea how to even start these problems? (1), at least, is almost trivial. I would expect a problem like that to be in an earlier chapter from (2) and (3). Please try. You learn mathematics by doing mathematics, not by watching others do it.
 
  • #3
ok thanks !i found the way !
 

FAQ: Calculating Volume Using Double Integrals: Finding the Boundaries and Limits

What is a double integral?

A double integral is a mathematical concept used to find the volume of a three-dimensional object. It involves calculating the area under a surface in two different directions.

How is a double integral used to find volume?

A double integral is used to find volume by dividing the object into small, measurable parts (typically rectangles) and summing up the areas of those parts. This process is repeated in both the x and y directions to find the total volume.

What is the notation for a double integral?

The notation for a double integral is ∫∫ f(x,y) dA, where f(x,y) represents the function being integrated and dA represents the differential of the area.

What is the difference between a single and double integral?

A single integral is used to find the area under a curve in one direction, while a double integral is used to find the volume under a surface in two directions.

What are some real-world applications of double integrals?

Double integrals have many real-world applications, such as calculating the volume of a solid object, finding the center of mass of an irregularly shaped object, and determining the probability of an event occurring in a two-dimensional space.

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