Concept explainers
Using the Fundamental Theorem for line
41.
Want to see the full answer?
Check out a sample textbook solutionChapter 17 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
Glencoe Math Accelerated, Student Edition
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Precalculus (10th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
- 5. Prove that the equation has no solution in an ordered integral domain.arrow_forwardPlant Growth Researchers have found that the probability P that a plant will grow to radius R can be described by the differential equation dPdR=4DRP2 where D is the density of the plants in an area. Source: Ecology. Given the initial condition P(0)=1, find a formula for P in term of R.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_forward
- Use the Fundamental Theorem to evaluate the definite integral exactly. 16 -xp- Enter the exact answer. 16 -dx = iarrow_forwardShow that the differential form in the integral below is exact. Then evaluate the integral. (5,-3,3) S 12x dx + 10y dy + 4z dz (0,0,0) Select the correct choice below and fill in any answer boxes within your choice. O A. (5,-3,3) S (0,0,0) (Simplify your answer. Type an exact answer.) 12x dx + 10y dy + 4z dz =arrow_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_forward
- Evaluate. 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_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_forwardsinx cosx - e +e sinx +* The integral dx may be written as me nsinx +px+ qe™ + C, sinx where m, n, p, q, r, and C are constants not equal to zero. Evaluate m+n+p+q +r.arrow_forward
- Verify 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. fv(e cos x) • dr, where C is the line from (0,0) to (2r, In 5) Select the correct choice below and fill in the answer box to complete your choice as needed. 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.) OB. The function is not conservative on its domain, and therefore, the Fundamental Theorem for line integrals cannot be used to evaluate the line integral.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_forwardUsing the Fundamental Theorem of Line Integrals, evaluate F. dr, where f(x, y, z) = cos(xx) + sin(xy) - xyz is a potential function for F, and C is any (1, 2). path that starts at and ends at (2, 5, -5).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,