# Area under graph when log-log scale gives straight line

1. Mar 5, 2009

### robsmith82

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

2. Mar 5, 2009

### HallsofIvy

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,
$$y= (e^{0.001})e^{\frac{0.0001(x-110)}{3}}$$

That should not be difficult to integrate.

3. Mar 5, 2009

### robsmith82

ok, i can integrate that, my real question is about how you found the function of y... How did you find that slope?