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Approximate the definite integral via the trapezoidal rule

Source: R/analysis_functions.R
trapezoidal_integration.Rd

Mostly meant for internal use in our analysis functions, but made available for other use cases. Accordingly, it does not strictly rely on objects of class muscle_stim.

Usage

trapezoidal_integration(x, f)

Arguments

x

a variable, e.g. vector of positions

f

integrand, e.g. vector of forces

Value

A numerical value indicating the value of the integral.

Details

In the functions analyze_workloop(), read_analyze_wl() , and read_analyze_wl_dir(), work is calculated as the difference between the integral of the upper curve and the integral of the lower curve of a work loop.

References

Atkinson, Kendall E. (1989), An Introduction to Numerical Analysis (2nd ed.), New York: John Wiley & Sons

See also

analyze_workloop, read_analyze_wl, read_analyze_wl_dir

Author

Vikram B. Baliga

Examples


# create a circle centered at (x = 10, y = 20) with radius 2
t <- seq(0, 2 * pi, length = 1000)
coords <- t(rbind(10 + sin(t) * 2, 20 + cos(t) * 2))


# use the function to get the area
trapezoidal_integration(coords[, 1], coords[, 2])
#> [1] 12.56629

# does it match (pi * r^2)?
3.14159265358 * (2^2) # very close
#> [1] 12.56637