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6) F(x, y, z) = (xy²z4, 2x²y+z, y³z²) a) Find curlF. b) Find divĒ.

6) F(x, y, z) = (xy²z4, 2x²y+z, y³z²) a) Find curlF. b) Find divĒ.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 97E
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Just answer question #6 please. Show full work.
1) ƒ_²₁ √ √√¹²(x² + y²) dxdydz Convert the integral to cylindrical coordinates and integrate. 2) ƒÑƒ (x² + y² + z²)² dv D is the unit ball. Integrate using spherical coordinates. 3) Evaluate f (xy + 2z) ds. C is the line segment from (1,0,0) to (0,1,1). 4) Use Green's Theorem to evaluate √ √1+x³dx + 2xydy. C is the triangle with vertices (0,0), (1,0), and (1,3). 5) Find the potential function of F(x, y, z) = (e²+ ye*, ex + zey, ey + xe² ). 6) F(x, y, z) = (xy²z4, 2x²y+z, y³z²) a) Find curlF. b) Find divF. 7) Use the double integral of a cross product to find the surface area of x = z² + y that lies between the planes y = 0, y = 2, z = 0, and z = 2.
Transcribed Image Text:1) ƒ_²₁ √ √√¹²(x² + y²) dxdydz Convert the integral to cylindrical coordinates and integrate. 2) ƒÑƒ (x² + y² + z²)² dv D is the unit ball. Integrate using spherical coordinates. 3) Evaluate f (xy + 2z) ds. C is the line segment from (1,0,0) to (0,1,1). 4) Use Green's Theorem to evaluate √ √1+x³dx + 2xydy. C is the triangle with vertices (0,0), (1,0), and (1,3). 5) Find the potential function of F(x, y, z) = (e²+ ye*, ex + zey, ey + xe² ). 6) F(x, y, z) = (xy²z4, 2x²y+z, y³z²) a) Find curlF. b) Find divF. 7) Use the double integral of a cross product to find the surface area of x = z² + y that lies between the planes y = 0, y = 2, z = 0, and z = 2.
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