45–50 Sketch the region of
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Chapter 15 Solutions
Calculus (MindTap Course List)
- Insect CannibalismIn certain species of flour beetles, the larvae cannibalize the unhatched eggs. In calculating the population cannibalism rate per egg, researchers need to evaluate the integral 0Ac(t)dt, where, A is the length of the larval stage and c(t) is the cannibalism rate per egg per larva of age t. The minimum value of A for the flour beetle Tribolium castaneum is 17.6 days, which is the value we will use. The function c(t) starts at day 0 with a value 0, increases linearly to the value 0.024 at day 12, and then stays constant. Source: Journal of Animal Ecology. Find the values of the integral using a. formula from geometry; b. the Fundamental Theorem of Calculus.arrow_forwardPlant Growth Researchers have found that the probability P that a plant will grow to radius R can be described by the differential equation dPdR=4DRP2 where D is the density of the plants in an area. Source: Ecology. Given the initial condition P(0)=1, find a formula for P in term of R.arrow_forwardConcentration of a solute According to the Ficks law, the diffusion of a solute across a cell membrane is given by c(t)=kAV[Cc(t)],(1) Where A is the area of the cell membrane, V is the volume of the cell, ct is the concentration inside the cell at time t, C is the concentration outside the cell, and k is constant. If co represents the concentration of the solute inside the cell when t = 0, then it can be shown that c(t)=(c0C)ekAt/V+C.(2) a. Use the last result to find c(t). b. Substitute back into Equation 1 to show that 2 is indeed the correct antiderivative of 1.arrow_forward
- ament 22 - Integration by Parts K www.aviatormast... Evaluate using integration by parts or substitution. Check by differentiating. (5x²-2x) ex dx [(5x²-2x) e 7x dx =arrow_forwardSketch the region of integration. 3 "y I 0 10 f(x, y) dx dyarrow_forwardsinx cosx - e +e sinx +* The integral dx may be written as me nsinx +px+ qe™ + C, sinx where m, n, p, q, r, and C are constants not equal to zero. Evaluate m+n+p+q +r.arrow_forward
- Sketch the region of integration and change the order of integration. 3 √9 - y² Br -3 JO f(x, y) dx dy f(x, y) dy dxarrow_forwardUsing the method of u-substitution, Se (6x - 8) dx = = [₁ f where U= du = a= b= f(u) = f(u) du (enter a function of x) da (enter a function of x) (enter a number) (enter a number) (enter a function of u). The value of the original integral is Note: You can earn full credit if the last answer box is correct and all other answer boxes are either blank or correct. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Email Instructorarrow_forwardx3 dx 4 + x Use integration by parts let u = x? dv = 4 + x2arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,