PrakKomstat_Pert 5

trapesium <-function(f, a, b, n) {
  h <- (b - a) / n
  jumlah <- 0
  for (i in 1:(n - 1)){
    jumlah <- jumlah + f(a + i * h)
  }
  I <- h / 2 * (f(a) + 2 * jumlah + f(b))
  return(I)
}
f<-function(t){2*t^2+1}
trapesium(f,0,6,6)

## [1] 152

turunan_maju <- function(f, x, h) {
  (f(x + h) - f(x)) / h
}
turunan_mundur <- function(f, x, h) {
  (f(x) - f(x - h)) / h
}
turunan_tengah <- function(f, x, h) {
  (f(x + h) - f(x - h)) / (2 * h)
}
turunan_kedua <- function(f, x, h) {
  (f(x + h) - 2 * f(x) + f(x - h)) / h^2
}
C <- function(t) { t^3 + 2 * t^2 }
turunan_maju(C, 2, 0.1)

## [1] 20.81

turunan_mundur(C, 2, 0.1)

## [1] 19.21

turunan_tengah(C, 2, 0.1)

## [1] 20.01

turunan_kedua(C, 2, 0.1)

## [1] 16

# Pembanding: turunan simbolik
d1 <- D(expression(t^3 + 2 * t^2), "t")
d1

## 3 * t^2 + 2 * (2 * t)

eval(d1, list(t = 2))

## [1] 20

d2 <- D(d1, "t")
d2

## 3 * (2 * t) + 2 * 2

eval(d2, list(t = 2))

## [1] 16

simpson <- function(f, a, b, n) {
  h <- (b - a) / n                  # lebar pias (n harus genap)
  ganjil <- 0
  genap <- 0
  for (i in 1:(n - 1)) {
    if (i %% 2 == 1) {
      ganjil <- ganjil + f(a + i * h)   # i = 1, 3, 5, ...
    } else {
      genap <- genap + f(a + i * h)     # i = 2, 4, 6, ...
    }
  }
  I <- h / 3 * (f(a) + 4 * ganjil + 2 * genap + f(b))
  return(I)
}
C <- function(t) { 10 * t * exp(-0.5 * t) }
simpson(C, 0, 4, 8)

## [1] 23.75731

interpolasi_linear <- function(x, y, x_target) { 
  if (x_target < min(x) || x_target > max(x)) {
    stop("Nilai target berada di luar rentang x")
  }
  
  # Cari dua titik x yang mengapit x_target
  for (i in 1:(length(x) - 1)) {
    if (x[i] <= x_target && x_target <= x[i + 1]) {
 # Lakukan interpolasi linier
 x1 <- x[i]
 x2 <- x[i + 1]
 y1 <- y[i]
 y2 <- y[i + 1]
 # Formula interpolasi linier
 y_target <- y1 + (y2 - y1) * ((x_target - x1) / (x2 - x1))
 return(y_target)
    }
  }
}

# Contoh data Z dan probabilitas
z_tabel <- c(-1.96, -1.64, -1.28, 0, 1.28, 1.64, 1.96)
alfa <- c(0.025, 0.05, 0.1, 0.5, 0.9, 0.95, 0.975)
# Target probabilitas yang ingin diinterpolasi
target_alfa <- 0.05

# Panggil fungsi interpolasi linier manual
z_estimate <- interpolasi_linear(alfa, z_tabel, target_alfa)

# Menampilkan hasil
z_estimate

## [1] -1.64