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- YOUR TURN Find the area under the curve y=sec2(x/3) between x= and 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_forwardWrite and evaluate the definite integral that represents the area of the surface generated by revolving the curve on the indicated interval about the x-axis. y = V 64 - x2, -7arrow_forwardEvaluate the given integral by making an appropriate change of variables. J Need Help? x - 5y 5 dA, where R is the parallelogram enclosed by the lines x - 5y = 0, x - 5y = 10, 7x - y = 9, and 7x - y = 10 7x - y Read It Watch It Master Itarrow_forwardShow that the differential form in the integral below is exact. Then evaluate the integral. Integral from left parenthesis 0 comma 0 comma 0 right parenthesis to left parenthesis 2 comma negative 4 comma 6 right parenthesis 2 x dx plus 10 y dy plus 14 z dz nbsparrow_forwardWrite and evaluate the definite integral that represents the area of the surface generated by revolving the curve on the indicated interval about the x-axis. y = V 49 - x2, -5 S x < 5 dx = J-5arrow_forwardWrite and evaluate the definite integral that represents the area of the surface generated by revolving the curve on the indicated interval about the x-axis. y = V 81 - x2, -7 SxS7 dx =arrow_forwardEvalua te the iterated integral. x+y dx dydz -2arrow_forward1 -dx Use the technique of completing the square to evaluate the following integral: J 2 - 6.xarrow_forwardDirection: Use substitution rule to evaluate the following integrals. 2x 1.5; dx 3. f- COSX 1+sinx dx 5. f 1+x² x² 2. √√dz dx 4. f (sinx + cos x)² dx 203 (²+1)20 dyarrow_forwardWrite and evaluate the definite integral that represents the area of the surface generated by revolving the curve on the indicated interval about the x-axis. y = V 49 – x², -5 < x s 5 dx = -5arrow_forwardBy converting the integral I= r drd® into Cartesian coordinates, we get: 4 dxdy +y the above integral None of these 4 - dxdy dxdy -1+x² the above integral the above integralarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,