Menghitung Luas Daerah di Bawah Kurva Fungsi Menggunakan Integral Tentu

Dosen Pengampu : Prof .Dr.Suhartono, M.Kom

Lembaga : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Fakultas : Sains dan Teknologi

Jurusan : Teknik Informatika

Kelas : (C) Kalkulus

NIM : 230605110080

library(mosaicCalc)

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library(ggplot2)

MENGHITUNG LUAS DAERAH DI BAWAH KURVA FUNGSI

Untuk menghitung luas daerah di bawah kurva fungsi menggunakan integral tentu, kita dapat menggunakan konsep dasar dari integral tentu. Misalnya, jika kita memiliki fungsi f(x) pada interval [a,b] dan kita ingin menghitung luas daerah di bawah kurva tersebut, kita dapat menggunakan rumus integral tentu sebagai berikut:

Luas = ∫ batas bawah a dan batas atas b f(x)dx

Sebagai contoh, misalkan kita ingin menghitung luas di bawah kurva fungsi f(x)=x^2 dari x=0 hingga x=2.

library(pracma)

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# Install dan load package pracma
install.packages("pracma")

## Warning: package 'pracma' is in use and will not be installed

library(pracma)

# Definisikan fungsi
f <- function(x) {
  return(x^2)
}

# Tentukan batas integral
a <- 0
b <- 2

# Hitung integral menggunakan fungsi integrate()
result <- integrate(f, lower = a, upper = b)

# Tampilkan hasil
print(paste("Luas daerah di bawah kurva:", result$value))

## [1] "Luas daerah di bawah kurva: 2.66666666666667"

# Install dan load package pracma
install.packages("pracma")

## Warning: package 'pracma' is in use and will not be installed

library(pracma)

# Definisikan fungsi
f <- function(x) {
  return(x^2)
}

# Tentukan batas integral
a <- 0
b <- 2

# Hitung integral menggunakan fungsi integrate()
result <- integrate(f, lower = a, upper = b)

# Buat grafik fungsi
x <- seq(0, 2, length.out = 100)
y <- f(x)

plot(x, y, type = "l", col = "blue", lwd = 2, xlab = "x", ylab = "f(x)", main = "Grafik f(x) = x^2")

# Tambahkan area di bawah kurva
polygon(c(a, x, b), c(0, y, 0), col = "skyblue")

# Tampilkan hasil integral sebagai teks pada grafik
text(1, 2, paste("Luas =", round(result$value, 2)), pos = 4, col = "red")

# Tampilkan grafik
grid()