Integral and Integration

Matkul : Kalkulus, Dosen Pengampu : Prof. Dr. SUHARTONO, M.Kom

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Integral adalah suatu fungsi yang digunakan untuk mengembalikan fungsi asli dari fungsi yang telah dibuat sebelumnya

library(mosaicCalc)

## Loading required package: mosaic

## Registered S3 method overwritten by 'mosaic':
##   method                           from   
##   fortify.SpatialPolygonsDataFrame ggplot2

## 
## The 'mosaic' package masks several functions from core packages in order to add 
## additional features.  The original behavior of these functions should not be affected by this.

## 
## Attaching package: 'mosaic'

## The following objects are masked from 'package:dplyr':
## 
##     count, do, tally

## The following object is masked from 'package:Matrix':
## 
##     mean

## The following object is masked from 'package:ggplot2':
## 
##     stat

## The following objects are masked from 'package:stats':
## 
##     binom.test, cor, cor.test, cov, fivenum, IQR, median, prop.test,
##     quantile, sd, t.test, var

## The following objects are masked from 'package:base':
## 
##     max, mean, min, prod, range, sample, sum

## Loading required package: mosaicCore

## 
## Attaching package: 'mosaicCore'

## The following objects are masked from 'package:dplyr':
## 
##     count, tally

## 
## Attaching package: 'mosaicCalc'

## The following object is masked from 'package:stats':
## 
##     D

f <- makeFun( A * x ^  2 ~ x, A = 0.5)
f(1)

## [1] 0.5

f(2)

## [1] 2

f(3)

## [1] 4.5

df <- D(f(x) ~ x)
df(1)

## [1] 1

df(2)

## [1] 2

df(3)

## [1] 3

slice_plot(f(x) ~ x, domain(x = -1:1), color = "blue") %>%
  gf_labs(title = "Original function f(x)")

slice_plot(df(x) ~ x, domain(x =-1:1), color = "purple") %>%
  gf_labs(title = "New function df(x), the derivative of f(x)")

slice_plot(df(x) ~ x, domain(x=-1:1), color = "red") %>%
  gf_labs(title = "Original function df(x)")

f1 <- makeFun(sin(x ^ 2) ~ x)
f2 <- makeFun(sin(x ^ 2)  +  3 ~ x)
f3 <- makeFun(sin(x ^ 2)  -  100 ~ x)
f1(1)

## [1] 0.841471

f2(1)

## [1] 3.841471

f3(1)

## [1] -99.15853

df1 = D(f1(x) ~ x)
df2 = D(f2(x) ~ x)
df3 = D(f3(x) ~ x)
df1(1)

## [1] 1.080605

df2(1)

## [1] 1.080605

df3(1)

## [1] 1.080605

fun = antiD( x^2 ~ x )
fun

## function (x, C = 0) 
## x^3/3 + C

fun(x = 2) - fun(x = -1)

## [1] 3

Daftar Pustaka : https://dtkaplan.github.io/RforCalculus/