Concept explainers
Evaluating line
a. Use a parametric description of C to evaluate the integral directly.
b. Use the Fundamental Theorem for line integrals.
29. φ(x, y) = x + 3y; C: r(t) = 〈2 – t, t〉, for 0 ≤ t ≤ 2
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Chapter 17 Solutions
Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package
Additional Math Textbook Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
University Calculus: Early Transcendentals (4th Edition)
Calculus & Its Applications (14th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
University Calculus: Early Transcendentals (3rd Edition)
- Use Green's Theorem to evaluate F. dr. (Check the orientation of the curve before applying the theorem.) F(x, y) = =(Vx + 4y3, 4x2 + C consists of the arc of the curve y = sin(x) from (0, 0) to (T, 0) and the line segment from (T, 0) to (0, 0)arrow_forward2.Proof that any tangent plane for the surface F( F) point = 0 passses through a fixedarrow_forwardUse Green's theorem to evaluate F. dr. (Check the orientation of the curve before applying the theorem.) F(x, y) = (y cos(x) – xy sin(x), xy + x cos(x)), Cis the triangle from (0, 0) to (0, 10) to (2, 0) to (0, 0)arrow_forward
- Use Green's theorem to evaluate F. dr. (Check the orientation of the curve before applying the theorem.) F(x, y) = (y cos(x) – xy sin(x), xy + x cos(x)), C is the triangle from (0, 0) to (0, 6) to (2, 0) to (0, 0) -arrow_forwardQ 2. Let C₁ be the straight line from the point (1,0) to the point (0, 1) in Figure 1. Let C₂ be an oriented and closed path in Figure 1. (a) (b) Evaluate the line integral of F = 4xi + 2xj along C₁. Evaluate the line integral of F = sin(2x)i + ej along C₂. Figure 1: A closed and oriented patharrow_forwardUse Green's Theorem to evaluate f, F •dr. (Check the orientation of the curve before applying the theorem.) F(x, y) = (y cos x xy sin x, xy + x cos x), C is the triangle from (0, 0) to (0, 4) to (2, 0) to (0, 0)arrow_forward
- find curl (curl F) = V x (V X F).arrow_forwardUse Green's Theorem to evaluate fa F. dr where F(x, y) = (y cos x, x² + 2y sin x) and C is the triangle from (0,0) to (2, 6), (2,6) to (2,0), and from (2, 0) back to (0,0). Make sure to check the orientation of the curve before applying Green's Theorem.arrow_forwardUse Green's theorem to evaluate F. dr. (Check the orientation of the curve before applying the theorem.) √(3 + ex²) dx + (tan−¹ (y) + 3x²) dy 3 y x² + y² = 16 2 x² + y² = 9 с 2 3 4arrow_forward
- Stokes' Theorem (1.50) Given F = x²yi – yj. Find (a) V x F (b) Ss F- da over a rectangle bounded by the lines x = 0, x = b, y = 0, and y = c. (c) fc ▼ x F. dr around the rectangle of part (b).arrow_forwardConsider the complex function f(z) = . Describe the level curves Zarrow_forwardUse Green's Theorem to evaluate So F. dr, where F =(√x+4y, 3x + √√ÿ) C consists of the arc of the curve y = 1x - x² from (0,0) to (1,0) and the line segment from (1,0) to (0,0).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
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