Green’s Theorem, circulation form Consider the following regions R and vector fields F . a. Compute the two-dimensional curl of the vector field. b. Evaluate both integrals in Green’s Theorem and check for consistency. 19. F = 〈 − 2 x y , x 2 〉 ; R is the region bounded by y = x (2 – x ) and y =0.
Green’s Theorem, circulation form Consider the following regions R and vector fields F . a. Compute the two-dimensional curl of the vector field. b. Evaluate both integrals in Green’s Theorem and check for consistency. 19. F = 〈 − 2 x y , x 2 〉 ; R is the region bounded by y = x (2 – x ) and y =0.
Green’s Theorem, circulation form Consider the following regions R and vector fields F.
a. Compute the two-dimensional curl of the vector field.
b. Evaluate both integrals in Green’s Theorem and check for consistency.
19. F =
〈
−
2
x
y
,
x
2
〉
; R is the region bounded by y = x(2 – x) and y=0.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Green’s Theorem, circulation form Consider the following regions R and vector fields F.a. Compute the two-dimensional curl of the vector field.b. Evaluate both integrals in Green’s Theorem and check for consistency.
F = ⟨2y, -2x⟩; R is the region bounded by y = sin x and y = 0, for 0 ≤ x ≤ π.
Channel flow The flow in a long shallow channel is modeled by the velocity field F = ⟨0, 1 - x2⟩, where R = {(x, y): | x | ≤ 1 and | y | < 5}.a. Sketch R and several streamlines of F.b. Evaluate the curl of F on the lines x = 0, x = 1/4, x = 1/2, and x = 1.c. Compute the circulation on the boundary of the region R.d. How do you explain the fact that the curl of F is nonzero atpoints of R, but the circulation is zero?
only solute question c , please
Chapter 17 Solutions
Calculus: Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
01 - What Is an Integral in Calculus? Learn Calculus Integration and how to Solve Integrals.; Author: Math and Science;https://www.youtube.com/watch?v=BHRWArTFgTs;License: Standard YouTube License, CC-BY