Nama : Muhammad Hafidlul Qolbi

NIM : 220605110063

Kelas : C

Mata Kuliah : Kalkulus

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

Jurusan : Teknik Informatika

Lembaga : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Latihan Soal Integral!!

Pertama!

riemann <- function(f, a, b, m = 100){
  n_width <- (b-a)/m
  x <- seq(a, b-n_width, length.out = m) + n_width/2
  y <- f(x)
  
  return(sum(y)*abs(b-a)/m)
}
riemann(function(x) x^2, a=0, b=1, m=2)
## [1] 0.3125
riemann(function(x) x^2, a=0, b=1, m=4)
## [1] 0.328125
riemann(function(x) x^2, a=0, b=1)
## [1] 0.333325

Kedua!!

trap <- function(f, a, b, m=100){
  x <- seq(a, b, length.out = m+1)
  y <- f(x)
  
  p_area <- sum((y[2:(m+1)] + y[1:m])) 
  p_area <- p_area * abs(b-a)/(2*m)
  return(p_area)
}
trap(function(x)x^2, a=0, b=1, m=2)
## [1] 0.375

Sumber Referensi:

https://bookdown.org/moh_rosidi2610/Metode_Numerik/diffinteg.html#newtoncotes