Integrales.R

library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.4.3

f1 <- function(x) ifelse(x >= 1 & x <= 6, 1/5, 0)
x1 <- seq(0, 7, length.out = 500)
y1 <- f1(x1)
df1 <- data.frame(x = x1,
                  y = y1)
ggplot(df1, aes(x = x,
                y = y)) +
  geom_line(color = "blue",
            size = 1.2) +
  geom_area(data = subset(df1, y > 0),
            fill = "skyblue",
            alpha = 0.5) +
  labs(title = "f(x) = 1/5 en [1,6]",
       x = "x", y = "f(x)") +
  theme_minimal()

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

# Calcular el valor de la integral en [0, 6]
area1 <- integrate(f1,
                  lower = 0,
                  upper = 6)$value
cat("Área bajo la curva en [a,b] =", area1, "\n")

## Área bajo la curva en [a,b] = 1

##########
f2 <- function(x) ifelse(x >= 0 & x <= 10, 2*x, 0)
x2 <- seq(0, 11, length.out = 500)
y2 <- f2(x2)
df2 <- data.frame(x = x2,
                  y = y2)
ggplot(df2, aes(x = x,
                y = y))+
  geom_area(data = subset(df2, y > 0),
            fill = "skyblue",
            alpha = 0.5) +
  labs(title = "f(x) = 2*x en [0,10]",
       x = "x", y = "f(x)") +
  theme_minimal()

# Calcular el valor de la integral en [0, 10]
area2 <- integrate(f2,
                   lower = 0,
                   upper = 10)$value
cat("Área bajo la curva en [a,b] =", area2/2, "\n")

## Área bajo la curva en [a,b] = 50

##########
f3 <- function(x) ifelse(x >= 4 & x <= 9, 3*x^2, 0)
x3 <- seq(0, 10, length.out = 500)
y3 <- f3(x3)
df3 <- data.frame(x = x3,
                  y = y3)
ggplot(df3, aes(x = x,
                y = y))+
  geom_area(data = subset(df3, y > 0),
            fill = "skyblue",
            alpha = 0.5) +
  labs(title = "f(x) = 3*x^2 en [4,9]",
       x = "x", y = "f(x)") +
  theme_minimal()

# Calcular el valor de la integral en [0, 10]
area3 <- integrate(f3,
                   lower = 0,
                   upper = 10)$value
cat("Área bajo la curva en [a,b] =", area3, "\n")

## Área bajo la curva en [a,b] = 665

##########
f4 <- function(x) ifelse(x >= 1 & x <= 6,
                         0.057803*(x^2+3), 0)
x4 <- seq(0, 10, length.out = 500)
y4 <- f4(x4)
df4 <- data.frame(x = x4,
                  y = y4)
ggplot(df4, aes(x = x,
                y = y))+
  geom_area(data = subset(df4, y > 0),
            fill = "skyblue",
            alpha = 0.5) +
  labs(title = "f(x) = k*(x^2+3) en [1,6]",
       x = "x", y = "f(x)") +
  theme_minimal()

# Calcular el valor de la integral en [1, 6]
area4 <- integrate(f4,
                   lower = 1,
                   upper = 6)$value
cat("Área bajo la curva en [a,b] =", area4, "\n")

## Área bajo la curva en [a,b] = 5.009593