PrakKomstat_Pert5

trapesium <- function(f, a, b, n) { 
  h <- (b - a) / n                       # lebar pias 
  jumlah <- 0 
  for (i in 1:(n - 1)) { 
    jumlah <- jumlah + f(a + i * h) # f(x1)+...+f(x(n-1)) 
  } 
  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

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

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

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