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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.arrow_forwardInsect 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_forward1. Use contour integration to evaluate the following integrals dx (1+x²)³ i. Sof x dx 11. S. (x² + 4X(X² +9) ii. please answer in typing format pleasearrow_forward
- Interchange the order of integration of the following integral (DO NOT EVALUATE). So St ex³ dz dyarrow_forwardEvaljate the integrjral using Integration by Parts. 2z2 cos 5z dzarrow_forwardFirst make a substitution and then use integration by parts to evaluate the integral. (Use C for the constant of integration.) t15 e-ts dtarrow_forward
- II. Perform the integration. 1. csc² x cot . tx/csc x – 1 dx |arrow_forwardy = x³ + 27 y 54 y = x° + 27 X 23 3 (a) Write the integral that describes the area of the shaded region. 0. dx (b) Find the area. (Give an exact answer. Do not round.)arrow_forwardvaluate the following integrals: ow CLEAN AND CLEAR solutions also indicate what rules/formulas you used to obtain your answ 4. S 2x2+4x-1 dx 2x-1 -2xarrow_forward
- A: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_forwardEvaluate the following integrals. 1 dx Use the method of completing the square. /24+10x –x² 4x² – 21x – 23 dx 4х +3 4x +5 x +9arrow_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 LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage