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Chapter 16 Solutions
CALCULUS:EARLY TRANSCENDENTALS-PACKAGE
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- 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_forwardTRANSFER TRAN SFER ACTIVITY 2: INTEGRATION THROUGH SUBSTITUTION Direction: Evaluate the following integrals. 1. S dx Vx 2. S dxarrow_forwardChange of variables Use the change of variables y4 = x² – 4 to evaluate the integral x Vx? – 4 dx.arrow_forward
- Q-1/ Evaluate the integral x?e*y dA y- 1 (2, 1) D D (0. 0)arrow_forward2e dx 2x +3 Evaluate the integralarrow_forwardSET-UP ONLY the definite integral that will give the area of the regionbounded by y = x + 1 and x = 1 − y2(a) using x as the variable of integration and(b) using y as the variable of integration.arrow_forward
- 13 2x To find the definite integral dx, apply the basic integration rule. X + 16 Let u = = x< + 16. Differentiate u in terms of x, du = 2 2 x dx. Step 2 Rewrite the integration in terms of u. 2x x= 3 du x² + 16 Jo Submit Skip (you cannot come back)arrow_forwardEvaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result. 2x dx Vx2 + 16 Step 1 2x To find the definite integral Vx + dx, apply the basic integration rule. + 16 Let u = x² + 16. Differentiate u in terms of x, du = A 2 x dx. Step 2 Rewrite the integration in terms of u. 2x x = 3 du V x2 + 16 = xp Step 3 Apply the power rule of integration. rx = 3 x = 3 du = du +1 1x = 3 +1Jo 1x = 3arrow_forwardEvaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result. 2x dx x2 + 16 Step 1 2x To find the definite integral dx, apply the basic integration rule. + 16 Let u = x2 + 16. Differentiate u in terms of x, du = 2 2 x dx. Step 2 Rewrite the integration in terms of u. 2x du dx = V x2 + 16arrow_forward
- Evaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result. 2x dx +16 Step 1 2x To find the definite integral dx, apply the basic integration rule. x² + 16 Let u = x + 16. Differentiate u in terms of x, du = 2 2 x dx. Step 2 Rewrite the integration in terms of u. x 3 1 1 du 2x x +16 Vu Step 3 Apply the power rule of integration. X= 3 x = 3 -1/2 -1/2 du du = -1/2 -1/2 + 17x = 3arrow_forwardEvaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result. 2x dx + 64 Step 1 6 2x To find the definite integral dx, apply the basic integration rule. + 64 Let u = x- + 64. Differentiate u in terms of x, du = 4 X 2 x dx. Step 2 Rewrite the integration in terms of u. 9. 2x Xx=6 dx = du x + 64arrow_forwardHW find the integration 3 dV 1-v²arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
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