Let I Be The The Intersection Of The Cylinder X Y 4 With The Plane X Y Z 0 And Let R Be The Part Of The Pla 1 (190.92 KiB) Viewed 41 times
Let I be the the intersection of the cylinder x² + y² = 4 with the plane x + y + z = 0, and let R be the part of the plane x + y + z = 0 that is enclosed inside the cylinder x² + y² = 4. (a) Find a continuously differentiable function : [0, 2π] → R³ that parametrizes l. (b) Evaluate the integral [(y² - a²)ds. (c) Find a continuously differentiable mapping r : D → R³, with D a Jordan domain in R², that parametrizes the surface R. [4] (d) Find the surface area of R. (e) Evaluate the surface integral (x² + y² + z²)do. Se R (f) Let F: R³ R³ be the vector field (e²² + y² +²² + y₂e²²+y² +²² — x, €²²+1²+z² + 2) · Y, tỷ F(x, y, z) = (e²³² + y² +² Use Stokes' formula to evaluate La curl F. do. [3] [6] [5] [5] [7]
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: [0, 2π] → R³ that parametrizes l. (b) Evaluate the integral [(y² - a²)ds. (c) Find a continuously differentiable mapping r : D → R³, with D a Jordan domain in R², that parametrizes the surface R. [4] (d) Find the surface area of R. (e) Evaluate the surface integral (x² + y² + z²)do. Se R (f) Let F: R³ R³ be the vector field (e²² + y² +²² + y₂e²²+y² +²² — x, €²²+1²+z² + 2) · Y, tỷ F(x, y, z) = (e²³² + y² +² Use Stokes' formula to evaluate La curl F. do. [3] [6] [5] [5] [7]