Evaluate the surface integral SF · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = yi − xj + 2zk, S is the hemisphere x2 + y2 + z2 = 4, z ≥ 0, oriented downward
Evaluate the surface integral
| S |
for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.
F(x, y, z) = yi − xj + 2zk, S is the hemisphere
Expert Answer
Want to see the step-by-step answer?
Evaluation Of Integral
Integral Calculus
Other
Related Advanced Math Q&A
Q: Help me fast so that I will give good rating.
A: Given system of equations dxdt=-2x-2ydydt=-2x+y can be written as X'=AX, A=-2-2-21, X=xy trA=-1 whe...
Q: please help me
A: We are given that S is a sphere of radius 5 . And also we are given the Equation of Sphere : x2+y2+z...
Q: Consider the position function s(t) = - 4.91² + 30t + 19. Complete the following table with the appr...
A: The average velocity over a interval of time is given as follows. Vavg=sb-sab-ast is th eposition ve...
Q: 1. Plot the following vectors using arrows on an xy-graph: -- (}). v-[+]. 1 u = V = 2u, u+v. Is ever...
A: Click to see the answer
Q: (1) Use induction to prove the following for all natural numbers n: 13 + 23 +... n3 n² (n+1)² 4
A: Click to see the answer
Q: Solve the following system of equations. – x + 2y + z = 2 – x + y + 2z = 5 y – z = 4 Whi...
A: Click to see the answer
Q: The loudness level of a sound, D, in decibels, is given by the formula: D = 10log(1012I) where I ...
A: Click to see the answer
Q: 10
A: The volume of a curve y=f(x) rotated about x axis on the interval a,b is given by the equation V=∫ab...
Q: Questions A and B please
A: Given, H=a+b+c+db-c+2da+2c-d: a,b,c,d∈ℝ⊆ℝ3 ⋯⋯(1) a) Given, u=111 Consider the system, a+b+c+db-...
