Volume Calculation Using Cylindrical Shells for Functions in First Quadrant

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In summary, double checking volume is a quality control measure used to ensure the accuracy of volume measurements. The process involves taking an initial measurement and then repeating it using a different method or instrument. This should be done whenever accuracy is critical, and periodically as part of routine quality control measures. Common methods for double checking volume include using a different instrument, measuring multiple times, or using a known volume for calibration. The benefits of double checking volume include ensuring accuracy and reliability, as well as identifying and correcting potential errors in the measurement process.
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Jbreezy
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Homework Statement



Consider the region between the functions f(x) = x^2 and g(x) = 2x in the first quadrant.
Use the method of cylindrical shells to find the volume generated by rotating about the y axis.
I did this integral
V = 2∏∫x(2x-x^2) dx between [0,2]
I got 2∏((2/3)x^3 - (x^4/4) = 8∏/3

Homework Equations



I think it is OK just want someone to confirm. Before I turn in.

The Attempt at a Solution

 
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  • #2
Looks fine to me.
 
  • #3
Thanks amigo.
 

1. What is the purpose of double checking volume?

Double checking volume is a quality control measure used to ensure the accuracy of volume measurements. It helps to identify any potential errors or inconsistencies in the measurement process.

2. How do you perform a double check volume?

The process of double checking volume involves taking the initial measurement, then repeating the measurement using a different method or instrument. The results of both measurements are then compared to ensure they are consistent.

3. What are some common methods for double checking volume?

Some common methods for double checking volume include using a different instrument to measure the same volume, measuring the same volume multiple times using the same instrument, or using a known volume to calibrate the instrument and then measuring the desired volume.

4. When should double checking volume be performed?

Double checking volume should be performed whenever accuracy is critical, such as in scientific experiments or industrial processes. It is also recommended to perform double checks periodically as part of routine quality control measures.

5. What are the benefits of double checking volume?

Double checking volume helps to ensure the accuracy and reliability of volume measurements, which is crucial in many scientific and industrial applications. It also helps to identify any potential errors or issues with the measurement process, allowing for corrections to be made and preventing costly mistakes.

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