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ex2yz2dSwhere S is the part of the cylinder Evaluate the surfacc integral S x229 between 0...
Evaluate the surface integral. 1. (x2+42+7) o ds S is the part of the cylinder x2 + y2 = 4 that lies between the planes z = 0 and 2 = 2, together with its top and bottom disks
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk, S is the part of the paraboloid z - x2 + y2, 251 (b) F(x, y, z) = (z, x-z, y), S is the triangle with vertices (1,0,0), (0, 1,0), and (0,0,1), oriented downward (c) F-(y. -x,z), S is the upward helicoid parametrized by r(u, v) = (UCOS v, usin v,V), osus 2, OSVS (Hint: Tu x Ty = (sin v, -cos v, u).)...
4. Evaluate the Surface Integral [f(r,y,0)nds , where S is the part of the surface z-Vx+y* below z-1, and i is the unit outer normal to S with negative z- component. 4. Evaluate the Surface Integral [f(r,y,0)nds , where S is the part of the surface z-Vx+y* below z-1, and i is the unit outer normal to S with negative z- component.
Evaluate the Surface Integral, double integral F*ds, where F = [(e^x)cos(yz), (x^2)y, (z^2)(e^2x)] and S is a part of the cylinder 4y^2 + z^2 =4 that lies above the xy plane and between x=0 and x=2 with upward orientation (oriented in the direction of the positive z-axis). ASAP PLEASE
Evaluate the following integral, ∫ ∫ S (x2 + y2 + z2) dS, where S is the part of the cylinder x2 + y2 = 25 between the planes z = 0 and z = 9, together with its top and bottom disks
= and z= 8. Let A be the part of the cylinder x2 + y2 1 between the planes z = 2, where n points away from the z-axis. Let C be the counterclockwise boundary of A. Let F(x, y, z) = (2xz + 2yz, –2xz, x2 + y²). Verify Stokes' Theorem: (a) Evaluate the line integral in Stokes' Theorem. (Hint: C has two separate parts.] (b) Evaluate the surface integral in Stokes' Theorem. Hint: curl (F) = (2x +...
11. Evaluate S. 'S*(1 + 3x2 + 2y?) dx dy. 12. Find the volume in the first octant of the solid bounded by the cylinder y2 + z2 = 4 and the plane x = 2y. Graph for Problem 12 13. Find the volume under the paraboloid z = 4 - x2 - y2 and above the xy-plane. N Consider the solid region bounded above by the sphere x + y + z = 8 and bounded below by the...
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) -xi yj+3 k S is the boundary of the region enclosed by the cylinder x2 + z2-1 and the planes y 0 and x y 2 Evaluate the surface integral F dS for the given vector field F and the oriented surface...
Find [(double integral) (ye^{x^2+z^2})dS], where S is the part of the surface of the cylinder x^2+z^2=9 that lies between y = 0 and y = 2. Please show how you parameterize the equation in cylindrical coordinates, as well as evaluating the integral.
Evaluate the following integral, ∫ ∫ S z dS, where S is the part of the sphere x2 + y2 + z2 = 16 that lies above the cone z = √ 3 √ x2 + y2 . Problem #6: Evaluate the following integral where S is the part of the sphere x2+y2 + z -y2 16 that lies above the cone z = 3Vx+ Enter your answer symbolically, as in these examples pi/4 Problem #6: Problem #6: Evaluate the...