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Multivariable Calculus (looseleaf)
- 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_forwardEvaluating Triple Iterated Integrals Evaluate the integrals in Exercises 7-20 10. $1 S S 0 JO cl ✓x²+3y² 3-3x 3-3x-y clc2 JU 0 dy dz dy dx du drarrow_forwardThe figure shows the sales growth rates under different levels of distribution and advertising from a to b. Set up an integral to determine the extra sales growth if $3 million is used in advertising rather than $2 million. (Use f for f(x), g for g(x), and h for h(x).) $4 Million advertising $3 Million 8 advertising $2 Million h advertising a Distribution dx Need Help? Read It Sales Growth Ratearrow_forward
- Evaluate the integral. Vx dx Need Help? Read It Watch It Talk to a Tutorarrow_forwardTRANSFER TRAN SFER ACTIVITY 2: INTEGRATION THROUGH SUBSTITUTION Direction: Evaluate the following integrals. 1. S dx Vx 2. S dxarrow_forwardEvaluate the integral below by interpreting it in terms of areas in the figure. The areas of the labeled regions are A1= 8, A2-4, A3-2 and A4=1 7 v = [₁² f(x)dx V = 10 A1 y=f(x) 3 A2 5 A3 7 A4 (figure is NOT to scale) 10arrow_forward
- 2e dx 2x +3 Evaluate the integralarrow_forwardI - 1 7. Evaluate the integral: dr. I (x + 1)² + 2arrow_forwardTutorial Exercise Write as a single integral in the form f(x) dx. f(x) dx + dx f(x) dx -5 Part 1 of 3 We know that for asbsc, f(x) dx + f(x) dx = f(x) dx. -5s1s 2, Using the first and second integrals, since we have dx + f(x) dx = f(x) dx. -5arrow_forward
- Using the method of u-substitution, 5 [²(2x - 7)² de where U = du: = a = b = f(u) = = ·b [ f(u) du a It (enter a function of x) da (enter a function of ä) (enter a number) (enter a number) (enter a function of u). The value of the original integral is 9.arrow_forwardThe figure shows the sales growth rates under different levels of distribution and advertising from a to b. Set up an integral to determine the extra sales growth if $4 million is used in advertising rather than $3 million. (Use f for f(x), g for g(x), and h for h(x).) $4 Million advertising $3 Million g advertising $2 Million h advertising Distribution dx Vi o! Sales Growth Rate | +| |x| |미 |5arrow_forwardTextbook Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the labeled regions are A1= 7, A2=3, A3=1 and A4=1 S (1 + f(x)) dx V= Videos [+] V = 10 Enter your answer as a whole number Question Help: Video 1 Video 2 Message instructor Submit Question Jump to Answer A1 y=f(x) A2 A3 7 A4 (figure is NOT to scale) 10arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,