Verifying Stoke’s Theorem In Exercises 3-6, verify Stoke’s Theorem by evaluating
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
Calculus (MindTap Course List)
- Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. ²dx + 2x²dy, where C is the square with vertices (0, 0), (3, 0). (3, 3), and (0, 3) oriented counterclockwise. fy²dx + 2x²dy =arrow_forwardEvaluate the line integral using Green's Theorem and check the answer by evaluating it directly. ∮C6 y2dx+3 x2dy∮C6 y2dx+3 x2dy, where CC is the square with vertices (0,0)(0,0), (3,0)(3,0), (3,3)(3,3), and (0,3)(0,3) oriented counterclockwise.arrow_forwardApplying the Fundamental Theorem of Line IntegralsSuppose the vector field F is continuous on ℝ2, F = ⟨ƒ, g⟩ = ∇φ, φ(1, 2) = 7, φ(3, 6) = 10, and φ(6, 4) = 20. Evaluate the following integrals for the given curve C, if possible.arrow_forward
- Help with thisarrow_forwardEvaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 6 y²dx + 2x²dy, where Cis the square with vertices (0, 0), (2, 0), (2, 2), and (0, 2) oriented counterclockwise. foy'dr + 2x*dy = i -128arrow_forwardhelp, I got this answer wrongarrow_forward
- Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise. 3 In(3 + y) dx - -dy, where C is the triangle with vertices (0,0), (6, 0), and (0, 12) ху 3+y ху dy = 3 In(3 + y) dx - 3+ yarrow_forwardEvaluating line integrals Evaluate the line integral ∫C F ⋅ drfor the following vector fields F and curves C in two ways.a. By parameterizing Cb. By using the Fundamental Theorem for line integrals, if possible F = ⟨y, z, -x⟩; C: r(t) = ⟨cos t, sin t, 4⟩ , for 0 ≤ t ≤ 2πarrow_forwardUsing the Fundamental Theorem for line integrals Verifythat the Fundamental Theorem for line integral can be used to evaluatethe given integral, and then evaluate the integral.arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning