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Find the area of the following surface using the given explicit description of...
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. f(xyz) = 4x,...
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. f(xyz) = 4x, where S is the cylinder X + z2-25, 0 ys2 The value of the surface integral is (Type exact answers, using T as needed.) Find the area of the following surface using the given explicit description of the surface. The cone z2 = (x2 +y2) , for Oszs8 Set up the surface integral for the given function over the given surface S as a...
Verify that the line integral and the surface integral of Stokes Theorem are equal far the following vector field, surface S, and closed curve C. Assume that C has counterlockwise orientation and S h...
Verify that the line integral and the surface integral of Stokes Theorem are equal far the following vector field, surface S, and closed curve C. Assume that C has counterlockwise orientation and S has a consistentorientation F = 〈y,-x, 11), s is the upper half of the sphere x2 + y2 +22-1 and C is the circle x2 + y2-1 in the xy-plane Construct the line integral of Stokes' Theorem using the parameterization r(t)= 〈cost, sint, O. for 0 sts2r...
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/...
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
1. Find the mass and centroid of the region bounded by the = y2 with p...
1. Find the mass and centroid of the region bounded by the = y2 with p (a, y) parabolas y x2 and x 2. Set up the iterated (double) integral(s) needed to calculate the surface area of the portion of z 4 2 that is above the region {(«, у) | 2, x < y4} R 2 Perform the first integration in order to reduce the double integral into a single integral. Use a calculator to numerically evaluate the single...
Find the surface area of each figure. Complete parts (a) through (e) below. cm The surface...
Find the surface area of each figure. Complete parts (a) through (e) below. cm The surface area of the cube is 06 Cm (Simplify your answer. Typical creacl answer using radicals as needed. Tyox anckach answer using as needed D. Right circular cylinder 1. CIEL The surface area of the right circular cylinder is em (Simplity your answer. Type an exact answer. Using rau ca s as needed. Type an exact answer, using as needed.) c. Right regular prisiti O...
Use a double integral to find the area of the region bounded by the cardioid r=...
Use a double integral to find the area of the region bounded by the cardioid r= -2(1 - cos 6). Set up the double integral as efficiently as possible, in polar coordinates, that is used to find the area. r drdo (Type exact answers, using a as needed.)
Oss4).Nor nal vectors po nt up e-zZxy across the curved sides of the surfa es-(xyz. z-cos y. y s: Find the flux of...
Oss4).Nor nal vectors po nt up e-zZxy across the curved sides of the surfa es-(xyz. z-cos y. y s: Find the flux of the vector field F= a Set up the integral that gives the flux as a double integral over a region R in the xy-plane. IIF.nds-IJO dA (Type exact answers.)
Oss4).Nor nal vectors po nt up e-zZxy across the curved sides of the surfa es-(xyz. z-cos y. y s: Find the flux of the vector field F= a...
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
2. Flux calculations: Set up the double integral for Js F.dA using cylindrical, spherical or shad...
Setup Only
2. Flux calculations: Set up the double integral for Js F.dA using cylindrical, spherical or shadow method as appropriate. ) s is the conical face z = v x2 +V2 over the region r 2 on the xy-plane, oriented downwards. (c
2. Flux calculations: Set up the double integral for Js F.dA using cylindrical, spherical or shadow method as appropriate.
) s is the conical face z = v x2 +V2 over the region r 2 on the...
Evaluate the surface integrat S «..z) ds using a parametric description of the surface S f(x,y.z)...
Evaluate the surface integrat S «..z) ds using a parametric description of the surface S f(x,y.z) = x2 +y? where S is the hemisphere x² + y² + z = 4, for z 20 Write a parametric description of the given hemisphere using u = p and v=0. rſu v)=000 where O susandsvs (Type exact answers.) The value of the surface integral is (Type an exact answer.)
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. f(xyz) = 4x, where S is the cylinder X + z2-25, 0 ys2 The value of the surface integral is (Type exact answers, using T as needed.) Find the area of the following surface using the given explicit description of the surface. The cone z2 = (x2 +y2) , for Oszs8 Set up the surface integral for the given function over the given surface S as a...
Verify that the line integral and the surface integral of Stokes Theorem are equal far the following vector field, surface S, and closed curve C. Assume that C has counterlockwise orientation and S has a consistentorientation F = 〈y,-x, 11), s is the upper half of the sphere x2 + y2 +22-1 and C is the circle x2 + y2-1 in the xy-plane Construct the line integral of Stokes' Theorem using the parameterization r(t)= 〈cost, sint, O. for 0 sts2r...
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
1. Find the mass and centroid of the region bounded by the = y2 with p (a, y) parabolas y x2 and x 2. Set up the iterated (double) integral(s) needed to calculate the surface area of the portion of z 4 2 that is above the region {(«, у) | 2, x < y4} R 2 Perform the first integration in order to reduce the double integral into a single integral. Use a calculator to numerically evaluate the single...
Find the surface area of each figure. Complete parts (a) through (e) below. cm The surface area of the cube is 06 Cm (Simplify your answer. Typical creacl answer using radicals as needed. Tyox anckach answer using as needed D. Right circular cylinder 1. CIEL The surface area of the right circular cylinder is em (Simplity your answer. Type an exact answer. Using rau ca s as needed. Type an exact answer, using as needed.) c. Right regular prisiti O...
Use a double integral to find the area of the region bounded by the cardioid r= -2(1 - cos 6). Set up the double integral as efficiently as possible, in polar coordinates, that is used to find the area. r drdo (Type exact answers, using a as needed.)
Oss4).Nor nal vectors po nt up e-zZxy across the curved sides of the surfa es-(xyz. z-cos y. y s: Find the flux of the vector field F= a Set up the integral that gives the flux as a double integral over a region R in the xy-plane. IIF.nds-IJO dA (Type exact answers.)
Oss4).Nor nal vectors po nt up e-zZxy across the curved sides of the surfa es-(xyz. z-cos y. y s: Find the flux of the vector field F= a...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
Setup Only
2. Flux calculations: Set up the double integral for Js F.dA using cylindrical, spherical or shadow method as appropriate. ) s is the conical face z = v x2 +V2 over the region r 2 on the xy-plane, oriented downwards. (c
2. Flux calculations: Set up the double integral for Js F.dA using cylindrical, spherical or shadow method as appropriate.
) s is the conical face z = v x2 +V2 over the region r 2 on the...
Evaluate the surface integrat S «..z) ds using a parametric description of the surface S f(x,y.z) = x2 +y? where S is the hemisphere x² + y² + z = 4, for z 20 Write a parametric description of the given hemisphere using u = p and v=0. rſu v)=000 where O susandsvs (Type exact answers.) The value of the surface integral is (Type an exact answer.)
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