- #1
karush
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$\displaystyle\pi\int_{0}^{\infty} e^x \ dx = \pi$
Ok I looked at some of the template equations but came up with this.
In summary, the conversation discusses a possible error in a given equation involving the integral of $e^{-2x}$, and how it should actually be $e^{2x}$. The error was caught by one of the participants, and they also discuss comparing the graphs in quadrant I to understand the issue.
$\displaystyle\pi\int_{0}^{\infty} e^x \ dx = \pi$
Ok I looked at some of the template equations but came up with this.
- #2
MarkFL
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I think you'd have the correct answer if the integrand is \(e^{-x}\), but as given the volume is unbounded.
- #3
skeeter
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if the curve is $y=e^{-x}$ ...
$\displaystyle V = \pi \int_0^\infty e^{-2x} \, dx = \dfrac{\pi}{2}$
$\displaystyle V = \pi \int_0^\infty e^{-2x} \, dx = \dfrac{\pi}{2}$
- #4
MarkFL
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skeeter said:
Yes, I overlooked the squaring of the radius.
- #5
karush
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why is it negative?
- #6
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It's a guess that the problem has a typo. The point is that \(\displaystyle e^{-2x}\) is bounded on \(\displaystyle [ 0, \infty )\) whereas \(\displaystyle e^{2x}\) is not.karush said:
-Dan
- #7
skeeter
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karush said:
compare the graphs in quadrant I ...
- #8
karush
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ok
glad you caught it
glad you caught it
- #9
skeeter
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karush said:
I didn’t catch the incorrect function ... mark did. see post #2.
Related to APC.5.2.01 AP Volume by Rotation
1. What is APC.5.2.01 AP Volume by Rotation?
APC.5.2.01 AP Volume by Rotation is a measurement used in radiology to assess the amount of air in the lungs. It is calculated by multiplying the cross-sectional area of the lungs by the distance between two slices on a CT scan.
2. Why is APC.5.2.01 AP Volume by Rotation important?
APC.5.2.01 AP Volume by Rotation is important because it can help diagnose and monitor lung diseases such as emphysema, chronic bronchitis, and asthma. It can also be used to evaluate the effectiveness of treatments for these conditions.
3. How is APC.5.2.01 AP Volume by Rotation measured?
APC.5.2.01 AP Volume by Rotation is measured using a CT scanner, which takes multiple images of the lungs at different angles. These images are then processed using specialized software to calculate the volume of air in the lungs.
4. What are the benefits of using APC.5.2.01 AP Volume by Rotation over other lung volume measurements?
APC.5.2.01 AP Volume by Rotation is considered a more accurate measurement of lung volume compared to other methods such as spirometry or chest x-rays. It provides a more detailed and comprehensive view of the lungs, allowing for better detection and monitoring of lung diseases.
5. Are there any risks or side effects associated with APC.5.2.01 AP Volume by Rotation?
APC.5.2.01 AP Volume by Rotation is a non-invasive procedure and does not have any known risks or side effects. However, as with any medical imaging test, there is a small amount of radiation exposure. The benefits of the test usually outweigh the potential risks.
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