Graphical Integration

Universitas : UIN Maulana Malik Ibrahim Malang

Prodi : Teknik Informatika

Fakultas : Sains dan Teknologi

Dosen : Prof. Dr. SUHARTONO, M.Kom

Graphical integration

Introduction

Graphical integration visually represents the process of finding the definite integral by calculating the area under the curve.

Riemann Sums for Graphical Integration

# Function to be integrated
f <- function(x) x^2 + 2*x + 1

# Riemann sum for graphical integration
riemann_graphical_integration <- function(f, a, b, n = 10) {
  delta_x <- (b - a) / n
  x_values <- seq(a, b, length.out = n)
  
  # Calculate the heights of rectangles
  heights <- f(x_values)
  
  # Plot the function
  plot(x_values, heights, type = "l", col = "blue", lwd = 2, main = "Graphical Integration", xlab = "x", ylab = "y")
  
  # Draw rectangles
  for (i in 1:n) {
    rect(x_values[i], 0, x_values[i + 1], heights[i], col = "skyblue", border = "black")
  }
  
  # Calculate and return the Riemann sum
  sum(heights * delta_x)
}

# Interval for integration
a <- 0
b <- 8

# Compute the Riemann sum for graphical integration
riemann_sum <- riemann_graphical_integration(f, a, b, n = 10)

riemann_sum

## [1] 252.1481