Exercise #5 Page 359 (Chapter 7):

Find the area of the shaded region in the given graph:

Based on the graph, the equation \(y=\frac{1}{2} x +3\) is above the equation \(y=\frac{1}{2} cosx +1\) in the interval \([0, 2 \pi]\)

SO, to calculate the area between the two equations, we simply integrate the difference between the two equations over the interval \([0, 2 \pi]\)

$$ $$

Let’s check the area using the “integrate” function:

# Define the function
f <- function(x) {
  return((1/2)*x + 3 - ((1/2)*cos(x) + 1))
}

# Perform the integration
result <- integrate(f, lower = 0, upper = 2 * pi)

# Print the result
print(result)
## 22.43598 with absolute error < 2.5e-13