48. Flour Beetles A model for describing the population of adult flour beetles involves evaluating the integral integrate (g(x))/x dx where g(x) is the per-unit-abundance growth rate for a popula- tion of size x. The researchers consider the simple case in which g(x) = a - bx for positive constants a and b. Find the integral in this case. Source: Ecology.

Now you'll evaluate the integral C 2y cos(7x) dx + 8xy dy on the closed curve C consisting of the line segments from (0,0) to (5,1) to (0,1) to (0,0) using Green's Theorem. Green's Theorem says this integral can be rewritten in the form integral D f(x, y) dA In this integral, f(x,y) = Setting up the double integral over the region D, you get integral A B integral c D f(x,y)dx dy (Note that the order of integration is specified--for this integral it will turn out that this is the easier order of integration). In this, A = B = C = D = Evaluating this integral, 2y cos(7x)dx + 8xydy = D f(x,y) dA =

Wters per How many lters leak out during the first hase? ou is Rounded to one decimal place a positive constant Consider the area under one arch of the curve no-7sin(be) for t z o where b is (o) Set up the definite Iintegral needed to find the area. dt dw (c) Write the definite integral in terms of w (d) Evaluate the integral in part (c). 卜 5 4 6