Section 13-1

course Mth 275

Section 13.1This section is clear and all of it makes sense. I had difficulty with only one of the problems. Number 36 states that R is a rectangular region with center at (0,0) and a population density r miles from the center = 12e^(-.07r) thousand people per square mile. It asks for the total population of the region as a double integral. I concluded that the region is a square with ?<=x<=r and ?<=y<=r. I substituted (x^2=y^2)^0.5 for r and wrote the integral as integral (from ? to r), integral (from ? to r) 12e^[-.07(x^2+y^2)^0.5]. Is this correct?

I believe so, but I can't read all your symbols.

Within an area increment of dimensions `dx by `dy, containing sample point (x, y), the area is `dA = `dx * `dy and the population is density * `dA = 12 exp(-.07 sqrt(x+2 + y^2) ) * `dx `dy. The Riemann sum therefore approaches the integral of 12 exp(sqrt(x^2 + y^2)); if the rectangle has dimensions 2 a by 2 b then the limits of the integral would be from -a to a with respect to x, and from -b to b with respect to y.

As a and b both approach infinity the integral converges.