Integral dan Diferensial

library(mosaicCalc)

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Diferensial

Untuk mendapatkan turunan dari fungsi dapat dengan menggunakan fungsi yang sudah disediakan oleh R yaitu D atau deriv Contoh :

Turunan dari f(x)=x2

xfs <- expression (exp(x^2))
D(xfs ,"x")

## exp(x^2) * (2 * x)

atau

xturunan <- deriv (~x^2,"x")
x <- 2
eval ( xturunan )

## [1] 4
## attr(,"gradient")
##      x
## [1,] 4

Integral

Untuk mendapatkan integral dari suatu fungsi, dapat menggunakan fungsi yang sudah disediakan oleh R yaitu fungsi integrate atau dengan menggunakan package Ryacas

Integral Tak Tentu Integral tak tentu dapat dicari dengan menggunakan fungsi yac_str. Contoh : 1. Integral dari f(x)=x2+4x

("Integrate(x) x^2 + 4*x")

## [1] "Integrate(x) x^2 + 4*x"

2. integral dari f(x)=t4exp(−t)

("Integrate(t) t^4 * Exp(-t)")

## [1] "Integrate(t) t^4 * Exp(-t)"

Integral Tentu

Integral tentu dapat dicari dengan menggunakan fungsi integrate.

1. Integral dari f(x)=x2+4x, dengan batas -10 sampai 10

f1 <-function(x) x^2 + 4*x
integrate(f1,lower = -10,upper = 10)

## 666.6667 with absolute error < 7.6e-12

2. Integral dari f(x)=t4exp(−t), dengan batas 0 sampai tak hingga

f2 <-function(t) t^(4) * exp(-t)
integrate(f2,lower = 0,upper = Inf)

## 24 with absolute error < 2.2e-05