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3. [4 marks] Using cylindrical polar coordinates, or otherwise, find the value of the surface integral...
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...
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.
Tutorial Exercise Use the Divergence Theorem to calculate the surface integral ss F. ds; that is,...
Tutorial Exercise Use the Divergence Theorem to calculate the surface integral ss F. ds; that is, calculate the flux of F across F(x,y,z) 3xy2 i xe7j + z3 k S is the surface of the solid bounded by the cylinder y2 + z2-4 and the planes x4 and x -4. Part 1 of 3 If the surface S has positive orientation and bounds the simple solid E, then the Divergence Theorem tells us that div F dV. For F(x, y,...
4. Using spherical coordinates, evaluate the triple integral: ry: dl, where E lies between the sp...
4. Using spherical coordinates, evaluate the triple integral: ry: dl, where E lies between the spheres r2+94:2-4 and r2+92+ะ2-16 and above the cone V+v) or Recommend separating! 5. Using spherical coordinates, find the volume of the solid that lies within the sphere r2+y2+2 9, above the ry-plane, and below the cone ะ-V/r2 + y2 Reconnnend separating! 6. Using spherical coordinates, evaluate the triple integral: 2 + dV where E is the portion of the solid ball 2+2+2 s 4 that...
Evaluate the surface integral F dot dS for the given vector field F and the oriented...
Evaluate the surface integral F dot 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.
24. F(x, y, z) = -xi - yj + z’k, S is the part of the cone z = x2 + y2 between the planes z 1 and 2 3 with downward orientation
Problem 3 (8 marks) Evaluate the surface integral JJz"(x+y*)dS , where S s the part of the plane ...
Problem 3 (8 marks) Evaluate the surface integral JJz"(x+y*)dS , where S s the part of the plane z 3 inside the paraboloid z = x2 + y2.
Problem 3 (8 marks) Evaluate the surface integral JJz"(x+y*)dS , where S s the part of the plane z 3 inside the paraboloid z = x2 + y2.
Dynamic 4. Compare rectangular coordinates with polar coordinates and cylindrical coordinates. Rectangular Cylindr...
Dynamic
4. Compare rectangular coordinates with polar coordinates and cylindrical coordinates. Rectangular Cylindrical Polar X, Y. Z R 5. For a circular motion, what are the normal and tangential components of the acceleration in the polar coordinates. Normal component ? Tangential component ? m
4. Compare rectangular coordinates with polar coordinates and cylindrical coordinates. Rectangular Cylindrical Polar X, Y. Z R 5. For a circular motion, what are the normal and tangential components of the acceleration in the polar coordinates....
Evaluate the surface integral (x2 + y' +52 ) ds where S is the part of the cone z = 2- x2 + y2 ab...
Evaluate the surface integral (x2 + y' +52 ) ds where S is the part of the cone z = 2- x2 + y2 above the z = 0 plane. The surface integral equals
Evaluate the surface integral (x2 + y' +52 ) ds where S is the part of the cone z = 2- x2 + y2 above the z = 0 plane. The surface integral equals
please just the final answer for both Evaluate the surface Integral || 5. ds for the...
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...
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.
Use cylindrical coordinates to find the volume of the cone shown in the figure:
Use cylindrical coordinates to find the volume of the cone shown in the figure: a) [3 points] Set up integral to find the volume b) [2 points] Evaluate the integralc) [5 points] Show that z = h(1-r/r0), where r is a radius of a circular cross-section of the cone parallel to xy-plane.
Tutorial Exercise Use the Divergence Theorem to calculate the surface integral ss F. ds; that is, calculate the flux of F across F(x,y,z) 3xy2 i xe7j + z3 k S is the surface of the solid bounded by the cylinder y2 + z2-4 and the planes x4 and x -4. Part 1 of 3 If the surface S has positive orientation and bounds the simple solid E, then the Divergence Theorem tells us that div F dV. For F(x, y,...
4. Using spherical coordinates, evaluate the triple integral: ry: dl, where E lies between the spheres r2+94:2-4 and r2+92+ะ2-16 and above the cone V+v) or Recommend separating! 5. Using spherical coordinates, find the volume of the solid that lies within the sphere r2+y2+2 9, above the ry-plane, and below the cone ะ-V/r2 + y2 Reconnnend separating! 6. Using spherical coordinates, evaluate the triple integral: 2 + dV where E is the portion of the solid ball 2+2+2 s 4 that...
Evaluate the surface integral F dot 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.
24. F(x, y, z) = -xi - yj + z’k, S is the part of the cone z = x2 + y2 between the planes z 1 and 2 3 with downward orientation
Problem 3 (8 marks) Evaluate the surface integral JJz"(x+y*)dS , where S s the part of the plane z 3 inside the paraboloid z = x2 + y2.
Problem 3 (8 marks) Evaluate the surface integral JJz"(x+y*)dS , where S s the part of the plane z 3 inside the paraboloid z = x2 + y2.
Dynamic
4. Compare rectangular coordinates with polar coordinates and cylindrical coordinates. Rectangular Cylindrical Polar X, Y. Z R 5. For a circular motion, what are the normal and tangential components of the acceleration in the polar coordinates. Normal component ? Tangential component ? m
4. Compare rectangular coordinates with polar coordinates and cylindrical coordinates. Rectangular Cylindrical Polar X, Y. Z R 5. For a circular motion, what are the normal and tangential components of the acceleration in the polar coordinates....
Evaluate the surface integral (x2 + y' +52 ) ds where S is the part of the cone z = 2- x2 + y2 above the z = 0 plane. The surface integral equals
Evaluate the surface integral (x2 + y' +52 ) ds where S is the part of the cone z = 2- x2 + y2 above the z = 0 plane. The surface integral equals
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...
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.
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