Evaluating a Line
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
Multivariable Calculus
- Determine whether the line integral of each vector field (in blue) along the semicircular, oriented path (in red) is positive, negative, or zero. Positive Positive Zero Zero Negative Positive - 1.arrow_forwardSplitting a vector field Express the vector field F = ⟨xy, 0, 0⟩in the form V + W, where ∇ ⋅ V = 0 and ∇ x W = 0.arrow_forwardSubject differential geometry Let X(u,v)=(vcosu,vsinu,u) be the coordinate patch of a surface of M. A) find a normal and tangent vector field of M on patch X B) q=(1,0,1) is the point on this patch?why? C) find the tangent plane of the TpM at the point p=(0,0,0) of Marrow_forward
- solve a part onlyarrow_forwardFlux across curves in a vector field Consider the vector fieldF = ⟨y, x⟩ shown in the figure.a. Compute the outward flux across the quarter-circleC: r(t) = ⟨2 cos t, 2 sin t⟩ , for 0 ≤ t ≤ π/2.b. Compute the outward flux across the quarter-circleC: r(t) = ⟨2 cos t, 2 sin t⟩ , for π/2 ≤ t ≤ π.c. Explain why the flux across the quarter-circle in the third quadrant equals the flux computed in part (a). d. Explain why the flux across the quarter-circle in the fourth quadrant equals the flux computed in part (b).e. What is the outward flux across the full circle?arrow_forwarddouble check work plsarrow_forward
- Applying 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_forwardEvaluating line integral, can u add explanation to question solutionarrow_forwardDetermine whether the line integral of each vector field (in blue) along the semicircular, oriented path (in red) is positive, negative, or zero. Positive Zero Positive Negative Negative 3. Negative 1 1 4arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning