Problem 15 (1 point) Use the divergence theorem to evaluate Is F N dS 2, บะ2,22).and N is the the unit outward normal to the surface Sgiven by z2 + y2trs where F-(r A.I 35 C. 1 = 35 (8)π Pro...
15. Use the Divergence Theorem to evaluate the surface integral F dS triple iterated integral where as a F= (-2rz 2yz, -ry,-xy 2rz - yz) and E is boundary of the rectangular box given by -1< x< 3, -1<y< 3 and z2 1 15. Use the Divergence Theorem to evaluate the surface integral F dS triple iterated integral where as a F= (-2rz 2yz, -ry,-xy 2rz - yz) and E is boundary of the rectangular box given by -1
Use the Divergence Theorem to evaluate F. N dS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results F(x, y, z) xyzj Use the Divergence Theorem to evaluate F. N dS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results...
Help Entering Answers (1 point) Use the Divergence Theorem to evaluate F . dS where F =くz2xHFz, y + 2 tan(2), X22-1 and S is the top half of the sphere x2 +y2 25 Hint: S is not a closed surface. First compute integrals over S and S2, where Si is the disk x2 +y s 25, z 0 oriented downward and s,-sus, F-ds, = 滋 dy dx F.dS2 = S2 where X1 = 리= Z2 = IE F-ds, =...
Provide correct answer Use the Divergence Theorem to evaluate //F. ds where F = (4x", 4y?, 17) and S is the sphere x² + y2 + z = 25 oriented by the outward normal. The surface integral equals
Divergence Theorem: Problem 4 Previous Problem Problem List Next Problenm (1 point) Evaluate JM F dS where F (3ay2,3a^y, z3) and M is the surface of the sphere of radius 2 centered at the origin. Divergence Theorem: Problem 4 Previous Problem Problem List Next Problenm (1 point) Evaluate JM F dS where F (3ay2,3a^y, z3) and M is the surface of the sphere of radius 2 centered at the origin.
(a) [4]Use the Divergence Theorem to prove that ſſF. n dS = 8, S where S is the surface of the cube -15 x 51, -15y51, -15 z 51 oriented outward, and F(x, y, z) = (4y2, 32-cosx, z’ - x). (b) [1] Would it have been easier to just calculate the given surface integral directly? Explain.
Use the Divergence Theorem to evaluate ∬SF⋅dS∬SF⋅dS where F=〈z2x,y33+3tan(z),x2z−1〉F=〈z2x,y33+3tan(z),x2z−1〉 and SS is the top half of the sphere x2+y2+z2=9x2+y2+z2=9. (1 point) Use the Divergence Theorem to evaluate FdS where F2x +3 tan2).^z-1 and S is the top half of the sphere x2 +y2 + z2 -9 Hint: S is not a closed surface. First compute integrals overs, and S2 , where S, is the disk x2 + y2 < 9, z = 0 oriented downward and S2 = S U...
Use the Divergence Theorem to evaluate S Ss F.dS where F= = (5x8, 6yz4, -40z?) and S is the boundary of the sphere 22 + y2 + z2 = 9 oriented by the outward normal. The surface integral equals
13. Show step by step how to use the Divergence Theorem to set up the surface integral F. dS := Fonds with outward orientation, where F(x, y, z) = (x, z, y) and S is the surface of the unit sphere x2 + y2 + z2 = 1. Do Not Evaluate.
1 point) Use Stoke's Theorem to evaluate (▽ × F)·dS where M is the hemisphere x2 + y2 + z2-16, x > 0, with the normal in the direction of the positive x direction, and F (x6,0,yl) Begin by writing down the "standard" parametrization of ЭМ as a function of the angle θ (denoted by "t" in your answer) a F-dsf(0) de, where f(θ) = The value of the integral is (use "" for theta). 1 point) Use Stoke's Theorem...