(See the 2 graphs in the attached question file)
I need to solve for the area under the 2 noted curves.
In the second graph, the beginning x,y coordinate is 5.0 minutes; 213 degrees; the ending x,y coordinate is 20.0 minutes; 393 degrees F.
[Please scroll to the end for an Update.] ****
Area under the curve = Integral (59.137 ln x + 82.276) dx over [0, 4.5]
= [Integral 59.137 ln x dx + Integral 82.276 dx] over [0, 4.5]
= [I1 + I2] over [0, 4.5]
Consider I1 = Integral 59.137 ln x dx = 59.137 * Integral ln x dx
We find the integral of ln x dx by integrating by parts, taking u as ln x and dv as dx
The solution file contains the calculation of area under the curves by integration. (This is part of a Physics experiment on pressure.)