Concept explainers
Using the Fundamental Theorem for line
40.
Want to see the full answer?
Check out a sample textbook solutionChapter 17 Solutions
EP CALCULUS:EARLY TRANS.-MYLABMATH 18 W
Additional Math Textbook Solutions
Calculus and Its Applications (11th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (4th 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_forwardVerify that the Fundamental Theorem for line integrals can be used to evaluate the following line integral, and then evaluate the line integral using this theorem. v(e -X sin y) • dr, where C is the line from (0,0) to (In 5,7) C Select the correct choice below and fill in the answer box to complete your choice as needed. O A. The Fundamental Theorem for line integrals can be used to evaluate the line integral because the function is conservative on its domain and has a potential function p(x,y) =| (Type an exact answer.) O B. The function is not conservative on its domain, and therefore, the Fundamental Theorem for line integrals cannot be used to evaluate the line integral. Click to select and enter vOur answer(s and then click Check Answerarrow_forward²6² F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. Je (4z + 4y) dx + (4x − 2z) dy + (4x − 2y) dz (a) C: line segment from (0, 0, 0) to (1, 1, 1) Evaluate (b) C: line segment from (0, 0, 0) to (0, 0, 1) to (1, 1, 1) (c) C: line segment from (0, 0, 0) to (1, 0, 0) to (1, 1, 0) to (1, 1, 1)arrow_forward
- Evaluate F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. (2z + 5y) dx + (5x – 4z) dy + (2x – 4y) dz (a) C: line segment from (0, 0, 0) to (1, 1, 1) (b) C: line segment from (0, 0, 0) to (0, 0, 1) to (1, 1, 1) (c) C: line segment from (0, 0, 0) to (1, 0, 0) to (1, 1, 0) to (1, 1, 1)arrow_forwardEvaluate fot F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. JC 1 [8(4x + 5y)i + 10(4x + 5y)j] · dr C: smooth curve from (-5, 4) to (3, 2) X Need Help? Read It Watch It Master Itarrow_forwardEvaluate. The differential is exact. HINT: APPLY: Fundamental theorem of line integral. The initial point of the path is (0,0,0) and the final point of the path is (4,5,1) (4.5, 1) (2x1²-2xz2²) dx + 2x²y dy-2x²z dz 10.00 768 OO 384 416arrow_forward
- Determine if Green's theorem can be used to evaluate the line integral. Then evaluate based on your finding. |(ex – 2y)dx + Iny dy, C: x=2cost, y= 3 + 2sint, Ost<2m Upload Choose a Filearrow_forwardUsing the Fundamental Theorem of Line Integrals, evaluate F. dr, where f(x, y, z) = cos(x) + sin(ay) – xyz is a potential (1, 2) function for F, and C is any path that starts at and ends at (2, 3, -2).arrow_forwardUsing 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_forward
- Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. $(5) (5x+ sinh y)dy - (3y² + arctan x²) dx, where C is the boundary of the square with vertices (1, 3), (2, 3), (2, 4), and (1,4). false (Type an exact answer.) (5x + sinh yldy – (3y® + arctan x an x²) dx = dx = ...arrow_forwardUse Green's theorem to evaluate the line integral along the given positively oriented curve. 1 yex yex dx + 2ex dy, C is the rectangle with vertices (0, 0), (4, 0), (4, 3), and (0, 3) Need Help? Read Itarrow_forwardUse Green's Theorem to evaluate the line integral along the given positively oriented curve. integral cos y dx + x2 sin y dy C is the rectangle with vertices (0, 0), (5, 0), (5, 4), (0, 4)arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage