Math Problem Statement
how is it 7.2649330114264
Solution
Let's go through the integration steps again to verify the calculations.
The integral setup for the volume is:
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Integrate with respect to :
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Integrate with respect to : Evaluating the antiderivative at the bounds:
For :
For :
So, the definite integral is:
- Integrate with respect to :
Evaluating the final numerical value:
Therefore, the volume of the solid is approximately .
The previous result of 7.2649330114264 seems to be incorrect based on this re-evaluation.
Do you have any more questions or need further details?
Here are 5 numbered questions you can ask:
- Can you explain how to integrate with respect to in cylindrical coordinates?
- How do cylindrical coordinates simplify solving volume integrals?
- What is the physical significance of the volume element in cylindrical coordinates?
- Can you provide examples of similar volume integration problems?
- How can we verify the results of such integrals?
Tip: Always double-check each step of integration, especially when converting bounds and evaluating definite integrals, to ensure accuracy.
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Math Problem Analysis
Mathematical Concepts
Integral calculus
Volume calculation
Cylindrical coordinates
Formulas
Volume integral formula in cylindrical coordinates
Theorems
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Suitable Grade Level
Advanced College
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