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Calculus: Early Transcendentals (2nd Edition)
- 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_forwardA:ME Assignment #8.. Code: ENG122 University of Mosul Mechanical Engincering Mathematics II Year:2020- 2021 Instructors: Dr, Omar Sallahaldeen and T.A. Suha Hashim ASSIGNMENT #8 Calculate the following integrals-: 9x- x - x 1- 2- 16x dx 4x - 4x + 1 3- 4- dy 5-arrow_forwardTRANSFER TRAN SFER ACTIVITY 2: INTEGRATION THROUGH SUBSTITUTION Direction: Evaluate the following integrals. 1. S dx Vx 2. S dxarrow_forward
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- Evaluate the integral by reversing the order of integration. 12 11e dx dy Need Help? Read It Watch Itarrow_forwardDetermine the x-coordinate of the centroid of the shaded area by integration. 29 y | Answer: x i 26 = 33 ----xarrow_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_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_forwardEvalulate the integral. (Use C for the constant integration.)arrow_forwardEvaluate the integral. (Remember the constant of integration.) I 4x 26 ²x+a+C + cx + C x + c dx X x Check your answer by taking the derivative.arrow_forward
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