Statement of the Problem

It is necessary to draw the graph and to show the table for function (the parameters are set by user)

\(y(x)=\sin(\cos(x \mu) \exp(-x/ \mu)),\) \(x \in [a,b], b=a+h.\)

Main Steps:

To choose \(a, h, \mu\)
To choose curve color
To study the behavior of function withdifferent parameters

Example of the Plot without Shiny

mu <- 3; a<-2; h<-3; color="red"
curve(sin(cos(mu*x)*exp(-x/mu)),a, a+h, n = 1001, 
      col=color, ylab="y(x)")

Example of the Table without Shiny

 x=seq(a,a+h,by=0.5); y=sin(cos(mu*x)*exp(-x/mu))
 data.frame(x,y)

##     x          y
## 1 2.0  0.4732425
## 2 2.5  0.1500779
## 3 3.0 -0.3289449
## 4 3.5 -0.1475431
## 5 4.0  0.2206077
## 6 4.5  0.1323552
## 7 5.0 -0.1429947

Example of the Plot the with Shiny

shiny application1

Example of the Table with Shiny

shiny application2

File ui.R

hinyUI(pageWithSidebar(
    headerPanel("Example of plotting function with parameter"),
  
    sidebarPanel(
              
        numericInput('a', 'Starting point a', 0, min = 0, max = 10),
        numericInput('h', 'Lenght of segment h', 1, min = 1, max = 10),
       
        sliderInput('mu', 'Parameter mu',
                    value = 2, min = 1, max = 5, step = 0.05),
        radioButtons('color', 'Curve color',
                    choices =   c("red", "blue", "green"))
    ),
    mainPanel(
        h4('y(x)=sin(cos(x*mu)*exp(-x/mu)), x in [a,a+h]'),
        tabsetPanel(
        tabPanel("Curve",plotOutput('myPlot')),
        tabPanel("Table", tableOutput("table"))
        ),
        h4('You entered'),
        h5('mu'),
        verbatimTextOutput("mu"),
        h5(' [a,a+h ] '),
        verbatimTextOutput("a_h")
    )
))

File server.R

library(shinyapps)

# Function with parameter
fun <- function(x,mu) 
    sin(cos(mu*x)*exp(-x/mu))

shinyServer(
    function(input, output) {
        # Generate function plot   
        output$myPlot <- renderPlot({
            mu <- input$mu
            a<-input$a
            h<-input$h
            curve(fun(x,mu), a, a+h, n = 1001, 
                  col=input$color, ylab="y(x)")
           })
    
    # Generate echo of user input
    output$mu <- renderPrint({input$mu})
    output$a_h <- renderPrint(paste0("x in [",{input$a},",",{input$a}+{input$h},"]"))
   
    # Generate table view of the function value
    output$table <- renderTable({
    mu <- input$mu
    a<-input$a
    h<-input$h
    x=seq(a,a+h,by=0.5)
    y=fun(x,mu)
    data.frame(x,y)
    })
})

Dinamic Plot and Table for Function with Parameter

Tetyna