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Fungsi dengan bahasa pemrograman R dan Python untuk menghitung:

1 Intergral Tentu dan Tak Tentu

Contoh Soal

Integral Tentu dan Tak Tentu

\(\left(\int_{-2}^{2}2x^6 +3\; dx\right)\)

\(\int 2x^6 +3\; dx\)

Fungsi=function(x){2*x^6+3}
Inten= integrate(Fungsi,lower=-2, upper=2)
Inten
## 85.14286 with absolute error < 9.5e-13
library(mosaicCalc)
## Loading required package: mosaicCore
## Registered S3 method overwritten by 'mosaic':
##   method                           from   
##   fortify.SpatialPolygonsDataFrame ggplot2
## 
## Attaching package: 'mosaicCalc'
## The following object is masked from 'package:stats':
## 
##     D
InTaTen= antiD(2*x^6+3~ x)
InTaTen
## function (x, C = 0) 
## 2/7 * x^7 + 3 * x + C

\[ \begin{align} \int 2x^6 +3\; dx&=\frac{2}{6+1}x^{6+1}+3x+c\\ &=\frac{2}{7}x^{7}+3x+c\\ \end{align} \]

2 Luas Lingkaran, Keliling Lingkaran, dan, Volume Bola.

\(LuasLingkaran =πr^2\)

\(KelilingLingkaran=2πr\)

\(VolumeBola=\frac{4}{3}πr^3\)

\(phi = \frac{22}{7}\)

Luas dan Keliling Lingkaran serta Volume Bola dengan phi = 22/7 dan r=14 adalah

phi = 22/7

LingBol= function(phi,r)
{
  Luas = phi*r^2
  Keliling= 2*phi*r
  Volume =round(4/3*phi*r^3, digits = 2)
  return(cat(c("Luas Lingkaran :",Luas,
               
               "Keliling Lingkaran :", Keliling,
               
               "Volume Bola:", Volume)))
  }
LingBol(22/7,14)
## Luas Lingkaran : 616 Keliling Lingkaran : 88 Volume Bola: 11498.67

3 Nilai Maksimum, Minimum, Rata-rata, Median, Mode, Variansi, Standard Deviasi pada data berfrekuensi.

\(Data.Berfrekuensi\)

Size = c(37,38,39,40,41,42)

Frekuensi = c(4,5,4,7,3,2)

df = data.frame(Size,
                Frekuensi)

df
##   Size Frekuensi
## 1   37         4
## 2   38         5
## 3   39         4
## 4   40         7
## 5   41         3
## 6   42         2
data = function(x,Frekuensi)
{maksimum = { DataUrut<-(sort(x,decreasing=F))
                                                tail(DataUrut,n=1)}
  minimum = tail(DataUrut,n=1)
  rata2= round(sum(x*Frekuensi)/sum(Frekuensi), digits=2)
  median <- {
  totfrek <- sum(Frekuensi)
  dataxy <- sort(rep.int(x,Frekuensi))
  ifelse(totfrek%%2==0, median <- ((dataxy[totfrek%/%2]/2) + (dataxy[totfrek%/%2]+1)/2),
         ifelse(totfrek%%2==1, 
  median <- ((dataxy[totfrek%/%2]))))}
  mode <- { 
    Jabar <- sort(rep.int(x,Frekuensi))
    nilai <- unique(Jabar)
    tab <-tabulate(match(Jabar,nilai))
    nilai[tab==max(tab)]}
  z=sum(Size*Frekuensi)
  xrat= z/(sum(Frekuensi))
  xminxrat= (Size-xrat)^2
  Frek.Rata=sum(Frekuensi*xminxrat)
  variansi <- Frek.Rata/sum(Frekuensi)
  standev <- sqrt(variansi)
  return(cat(c("Nilai Maksimum =",     maksimum,
               "Nilai Minimum =", minimum,
               "rata-rata =", rata2,
               "Median=", median,
               "Modus=", mode,
               "Variansi=",variansi,
               "Standar Deviasi",standev
               )))
}
data(df$Size,df$Frekuensi)
## Nilai Maksimum = 42 Nilai Minimum = 42 rata-rata = 39.24 Median= 39 Modus= 40 Variansi= 2.2624 Standar Deviasi 1.50412765415705