How to calculate the AUC using trapezoidal rule in R

Recipe Objective

How to calculate the AUC using trapezoidal rule in R.

The trapezoidal rule evaluates the AUC — area under the curve by dividing the curve's total area into small trapezoids rather than dividing into small rectangles. This recipe explains how to calculate the AUC using trapezoidal rule in R.

Step 1 - Use trapz()

trapz(x,y) where, x : the coordinates of points on the x-axis. y: the y - coordinates of function values.

n <- 100 x <- seq(0, pi, len = n) y <- sin(x) trapz(x, y) # AUC for sin function graph ranging from 0 - pi value

"Output is : 1.99983216389399" 

n <- 100 x <- seq(0, pi, len = n) y <- cos(x) trapz(x, y) # AUC for cos function graph ranging from 0 - pi value

"Output is : 3.67761376907083e-16"

n <- 100 x <- seq(0, pi, len = n) y <- tan(x) trapz(x, y) # AUC for tan function graph ranging from 0 - pi value

"Output is : 1.55245824876027e-14 "

n <- 100 x <- seq(0, 1, len = n) y <- x*x trapz(x, y) # AUC for x-square, graph ranging from 0 - 1 value

"Output is : 0.333350338400844 "

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