Area under graph when log-log scale gives straight line

In summary, the conversation discusses a graph with logarithmic scales and a straight line between two points. The goal is to find the area under the graph and the method involves finding the function of the line and evaluating a definite integral. The participant also asks about the process of finding the function of the line.
  • #1
robsmith82
17
0
Hi,

I have a graph with a frequency on the x-axis and power density on the y axis. Both scales are logarithmic, and the graph shows a straight line between the points (110Hz, 0.001V^2/Hz) and (200Hz, 0.004V^2/Hz). I need to work out the area under this portion of the graph as it relates to total power.

So, my understanding is I need to find the function of the line, then set up and evaluate a definite intergral between 110Hz and 200Hz. My real question is, how do I work out the function of the line, and is this a correct method?

Thanks

Rob
 
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  • #2
That straight line has slope .0001/3 and passes through 0(110Hz, 0.001) so has equation log(y)= (0.0001/3)(x- 110)+ 0.001. Taking exponentials of both sides,
[tex]y= (e^{0.001})e^{\frac{0.0001(x-110)}{3}}[/tex]

That should not be difficult to integrate.
 
  • #3
ok, i can integrate that, my real question is about how you found the function of y... How did you find that slope?
 

Related to Area under graph when log-log scale gives straight line

1. What is the significance of using a log-log scale when plotting a graph?

Using a log-log scale on a graph allows for a better visualization of relationships between variables that have a wide range of values. It compresses the data towards the axes, making it easier to see patterns and trends.

2. How do I calculate the area under a graph when using a log-log scale?

To calculate the area under a graph on a log-log scale, you can use the trapezoidal rule or Simpson's rule. These numerical integration methods take into account the curved nature of a log-log graph and provide a more accurate estimation of the area.

3. Can a curve on a log-log graph also be considered a straight line?

Yes, a curved line on a log-log graph can appear as a straight line if the relationship between the variables is a power law. This means that one variable is proportional to a power of the other, and when plotted on a log-log scale, it appears as a straight line.

4. What does it mean if the area under a log-log graph is zero?

If the area under a log-log graph is zero, it means that there is no relationship between the variables being plotted. This could be due to a lack of data or a weak correlation between the variables.

5. Is the area under a log-log graph affected by the scaling of the axes?

Yes, the area under a log-log graph will be affected by the scaling of the axes. Changing the scale can alter the visual appearance of the graph and change the calculated area. It is important to carefully choose the scale to accurately represent the relationship between the variables.

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