Focus on Calculus

in Geography

Rotate the map of the continental United States so that Florida points straight down. So the

country can be reasonably represented as a region bounded by two functions N(x) and S(x),

where N(x) is the northern boundary of the rotated U.S. and S(x) is the southern boundary of the rotated U.S. (see Figure below).

Question 1: Assuming the side length of each square on the grid corresponds to A miles, if x = a and x = b are the western and eastern most extremities, respectively, of the rotated U.S. in the figure below, express an estimate of the area of the U.S. as a definite integral in terms of A, N(x), and S(x).

Question 2: How does this Focus on Calculus apply to Calculus?

Figure: Rotated United States

Focus on Calculus in Geography Rotate the map of the continental United States so that Florida points straight down. So the country can be reasonably represented as a region bounded by two functions N(x) and S(x), where N(x) is the northern boundary of the rotated U.S. and S(x) is the southern boundary of the rotated U.S. (see Figure below). Question 1: Assuming the side length of each square on the grid corresponds to A miles, if x = a and x = b are the western and eastern most extremities, respectively, of the rotated U.S. in the figure below, express an estimate of the area of the U.S. as a definite integral in terms of A, N(x), and S(x). Question 2: How does this Focus on Calculus apply to Calculus? Figure: Rotated United States . L- N(x) S(x)