Surface D is given by r(u, v) = u, v, u2 + v^2 , above the solid circle x 2 + y 2 ≤ 2, oriented upwards. The vector field F is (x^2 , xz, y2*z). Set up a double integral with the same value as Z ∂D F · dr, so that the integral is ready to evaluate. Do not evaluate either integral.
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Help would be greatly appreciated!! 1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped like a parallelogram, and its boundary aS (with positive orientation) is made up of four line segments. Compute the line integral fos F -dr where F(z, y, z) = 〈エ2018 + y, 2r, r2-Ins). Hint: use Stokes' theorem to transform this...
F·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) Evaluate the surface integral orientation. F(x, y, z) -x2i +y^j+z2 k S is the boundary of the solid half-cylinder 0szs V 25 -y2, 0 sxs2 Need HelpRead It Watch Talk to a Tutor F·dS for the given vector field F and the oriented surface S. In other words, find the flux...
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be the hemisphere 2 F(x, y,z)-yitj+3z k. Calculate JJs F dS, the flux of F across S 7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be...
Sle Evaluate the surface integral F.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) = x2 i + y2 j + z2 k S is the boundary of the solid half-cylinder OSZS25 - y2,0 5x54 250 x
Il Evaluate the surface integral F.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) = y) - zk, S consists of the paraboloid y = x2 + 22,0 Sys1, and the disk x2 + z2 s 1, y = 1. Evaluate the surface integral F.ds for the given vector field F and the oriented surface S....
Evaluate the surface integral F.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 + Szk, S is the hemisphere x2 + y2 + z2 = 4, z 20, oriented downward -8751 x
1 Help Entering Answers 1 point) Use Stokes' Theorem to evaluateF.dr where F(x,y,z) 6yzi 3xzj +3e k and C is the circy4,z 5 oriented counterclockwise as viewed from above Since the circle is oriented counterclockwise as viewed from above the surface we attach to the circle is oriented upwards The easiest surface to attach to this curve is the disk x2 + y2 < 4, z-5. Using this surface in Stokes' Theorem evaluate the following. F-dr = where sqrt(4-xA2) sqrt(4-x^2)...
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly, b) using Green's Theorem, where C consists of the arc of the parabola y = x2 from (0,0) to (2,4) and the line segments from (2,4) to (0,4) and from (0,4) to (0,0). [Answer: 0] Q2. Use Green's Theorem to evaluate the line integral $. F. dr or the work done by the force field F(x, y) = (3y - 4x)i +(4x - y)j...
please just the final answer for both Evaluate the surface Integral || 5. ds for the given vector fleld 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 + Szk, S is the hemisphere x2 + y2 + y2 = 4, 220, oriented downward 26.677 X Evaluate the surface integral llo F.ds for the given vector field F...
please help with Q1 and 3 1. Let V be the solid region in R3 that lies within the sphere 2+y+z2-4, above the zy-plane, and below the cone z -Vx2 + y2 (a) Sketch the region V (b) Calculate the volume of V by using spherical coordinates. (c) Find the surface area of the part of V that lies on the sphere z2 y 24, by calculatinga surface integral. (d) Verify your solution to (c) by calculating the surface integral...