Integration concept check

In summary, the question is asking for an integral to find the volume inside the cone z=r, above the xy-plane, and inside the sphere x^2 + y^2+z^2 = 8. However, the cone in question is actually the volume outside the cone, but inside the hemisphere of the sphere. It may be helpful to draw a sketch to better understand the orientation of the cone. So the volume that needs to be calculated is not below the cone or inside the cone, but outside the cone.
  • #1
stratusfactio
22
0
The question asks to find an integral that gives the specified volume

below the cone z=r, above the xy-plane, and inside the sphere x^2 + y^2+z^2 = 8.

So essentially, we're finding the volume inside the cone? I know that the very top of the cone would include the top of the sphere.

So does below cone = inside cone?
 
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  • #2
stratusfactio said:
The question asks to find an integral that gives the specified volume

below the cone z=r, above the xy-plane, and inside the sphere x^2 + y^2+z^2 = 8.

So essentially, we're finding the volume inside the cone?
No, it's the volume outside the cone, but inside the hemisphere. The cone comes to a point at the origin, and gets larger as z increases.
stratusfactio said:
I know that the very top of the cone would include the top of the sphere.
Have you drawn a sketch of the situation? I don't think you have a good idea of the orientation of the cone.
stratusfactio said:
So does below cone = inside cone?
No, outside the cone.
 

What is integration concept check?

Integration concept check is a process that involves evaluating how well different components or systems work together to achieve a specific goal or function.

Why is integration concept check important?

Integration concept check is important because it helps ensure that all components are functioning properly and working together seamlessly to achieve the desired outcome. It also helps identify any potential issues or conflicts that may arise during the integration process.

What are the steps involved in integration concept check?

The steps involved in integration concept check may vary depending on the specific project or system, but generally involve planning and design, testing and validation, and continuous monitoring and maintenance.

How is integration concept check different from other types of testing?

Integration concept check focuses specifically on how different components work together, while other types of testing may focus on individual components or functions. Integration concept check is also typically done after each component has been tested individually.

What are some common challenges in integration concept check?

Some common challenges in integration concept check include communication and coordination among team members, compatibility issues between different components, and identifying and resolving any conflicts or errors that may arise during the integration process.

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