CODEWITHSUNDEEP
rderivativeintegrallongitudinal
Lisa
Lisa

Reputation: 131

how to get the area under the curve or integral in r

I have a curve as the data below and I would like to calculate the area under the curve (integral) of this curve made by x and y points. Is it correct to do in the way below? and how can I calculate the area under the curve within a specific interval without knowing the function of curve? I am going to repeat this with the rest of my data for each individual with repeated measurements. Also, I need to calculate the area under the curve for the first and second derivative values. should I do the same? Thank you for your advice.

structure(list(x = c("76.37", "76.89", "77.36", "77.86", "78.86", 
                 "79.37", "79.87", "80.36", "80.5", "81.2"), 
           y = c("2.1", "2.29", "2.47", "2.65", "2.82", "2.99", "3.16", "3.31", "3.46", "3.5")), 
      class = c("tbl_df", "tbl", "data.frame"), row.names = c(NA,-10L))


library(pracma)
AUC = trapz(data$x,data$y)

Upvotes: 1

Views: 646

Answers (1)

Onyambu
Onyambu

Reputation: 79228

You could approximate the function thus use approxfun with a linear interpolation

integrate(approxfun(df$x, df$y), min(df$x), max(df$x))
13.78885 with absolute error < 0.00049

Note that a rough approximation of the area yields a number closer to this. This assumes the region is trapezoidal.

prod(sapply(df, \(x)diff(range(x))))/2 + diff(range(df$x)) * min(df$y)
[1] 13.524

Upvotes: 1

Related Questions