![8) [10 points] Use a surface integral to find the mass of the surface lamina Зл r(u, v)=sin v cosui+sin vsin uj+cos vk where](http://img.homeworklib.com/questions/e8d531c0-ac5a-11eb-9cd1-8b2bed8650c3.png?x-oss-process=image/resize,w_560)
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8) [10 points] Use a surface integral to find the mass of the surface lamina Зл...
D . Problem 4. A lamina lies in the first quadrant and is enclosed by the...
D . Problem 4. A lamina lies in the first quadrant and is enclosed by the circle x2 +y2 = 4 and the lines x = 0 and y = 0. The density function of the lamina is equal to p(x, y) = V x2 + y2. Use the double integral formula in polar coordinates, S/ s(8,y)dx= $." \* fcr cos 6,r sin Øyrar] de, Ja [ Ꭱ . to calculate (1) the mass of the lamina, m = SSP(x,y)...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk,...
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).)...
Find the area of the surface over the given region. Use a computer algebra system to verify your results. The torus r(u, v)-(a + b cos v)cos ui + (a + b cos v)sin uj + b sin vk, where a > b, 0 2 π...
Find the area of the surface over the given region. Use a computer algebra system to verify your results. The torus r(u, v)-(a + b cos v)cos ui + (a + b cos v)sin uj + b sin vk, where a > b, 0 2 π, b > 0, and 0 2π u v
Find the area of the surface over the given region. Use a computer algebra system to verify your results. The torus r(u, v)-(a + b cos...
Evaluate the surface integral. y ds, S is the helicoid with vector equation r(u, v) =...
Evaluate the surface integral. y ds, S is the helicoid with vector equation r(u, v) = (u cos(V), u sin(), v), OSUS 4,0 SV S.
Evaluate the surface integral SS -?yds Where S :r(u, v) = 5 cosui +5sinu j+ vk,...
Evaluate the surface integral SS -?yds Where S :r(u, v) = 5 cosui +5sinu j+ vk, Osus, osvsi S
first picture is all the questions that need to be answered, second is the actual numbers...
first picture is all the questions that need to be answered,
second is the actual numbers being used
17.6.25-Setup & Solve Evaluate the surface integral s Srixy.z) ds using a parametric description of the surface S f(xy.z) = 4x² + 4y?, where S is the hemisphere x² + y² +z? = 4, for z 20 Write a parametric description of the given hemisphere using u = Q and v = 0. I r(u,v) = (2 sin ucos V.2 sin usin...
A. Find the center of mass for lamina defined by the interior of the polar curve r=sin(3) with a ...
a. Find the center of mass for lamina defined by the interior of
the polar curve r=sin(3) with a density
that varies according to p(r,theta)=1/r
b. Find the volume of the cylinder inside the sphere
For part a I got a mass of 2 but not sure about the x bar and y
bar calculations.
For part b Im stuck on the z bounds for the integral when doing
the problem with the cylindrical coordinate method.
We were unable to...
Evaluate the surface integral. 1 (x + y + z) ds, S is the parallelogram with...
Evaluate the surface integral. 1 (x + y + z) ds, S is the parallelogram with parametric equations x = u + v, y = u - v, z = 1 + 2 + v, osus 6, Osvs 2.
40 1. 16 pts) Evaluate the integral( quadrant enclosed by the cirle x + y2-9 and the lines y - 0 ...
Please do #2
40 1. 16 pts) Evaluate the integral( quadrant enclosed by the cirle x + y2-9 and the lines y - 0 and y (3x-)dA by changing to polar coordinates, where R is the region in the first 3x. Sketch the region. 2. [6 pts) Find the volume below the cone z = 3、x2 + y2 and above the disk r-3 cos θ. your first attempt you might get zero. Think about why and then tweak your integral....
Evaluate the surface integral. (x + y + z) ds, S is the parallelogram with parametric...
Evaluate the surface integral. (x + y + z) ds, S is the parallelogram with parametric equations x = u + v, y = u – v, z = 1 + 2u + v, Osus 6, 0 SV 53. Is
D . Problem 4. A lamina lies in the first quadrant and is enclosed by the circle x2 +y2 = 4 and the lines x = 0 and y = 0. The density function of the lamina is equal to p(x, y) = V x2 + y2. Use the double integral formula in polar coordinates, S/ s(8,y)dx= $." \* fcr cos 6,r sin Øyrar] de, Ja [ Ꭱ . to calculate (1) the mass of the lamina, m = SSP(x,y)...
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).)...
Find the area of the surface over the given region. Use a computer algebra system to verify your results. The torus r(u, v)-(a + b cos v)cos ui + (a + b cos v)sin uj + b sin vk, where a > b, 0 2 π, b > 0, and 0 2π u v
Find the area of the surface over the given region. Use a computer algebra system to verify your results. The torus r(u, v)-(a + b cos...
Evaluate the surface integral. y ds, S is the helicoid with vector equation r(u, v) = (u cos(V), u sin(), v), OSUS 4,0 SV S.
Evaluate the surface integral SS -?yds Where S :r(u, v) = 5 cosui +5sinu j+ vk, Osus, osvsi S
first picture is all the questions that need to be answered,
second is the actual numbers being used
17.6.25-Setup & Solve Evaluate the surface integral s Srixy.z) ds using a parametric description of the surface S f(xy.z) = 4x² + 4y?, where S is the hemisphere x² + y² +z? = 4, for z 20 Write a parametric description of the given hemisphere using u = Q and v = 0. I r(u,v) = (2 sin ucos V.2 sin usin...
a. Find the center of mass for lamina defined by the interior of
the polar curve r=sin(3) with a density
that varies according to p(r,theta)=1/r
b. Find the volume of the cylinder inside the sphere
For part a I got a mass of 2 but not sure about the x bar and y
bar calculations.
For part b Im stuck on the z bounds for the integral when doing
the problem with the cylindrical coordinate method.
We were unable to...
Evaluate the surface integral. 1 (x + y + z) ds, S is the parallelogram with parametric equations x = u + v, y = u - v, z = 1 + 2 + v, osus 6, Osvs 2.
Please do #2
40 1. 16 pts) Evaluate the integral( quadrant enclosed by the cirle x + y2-9 and the lines y - 0 and y (3x-)dA by changing to polar coordinates, where R is the region in the first 3x. Sketch the region. 2. [6 pts) Find the volume below the cone z = 3、x2 + y2 and above the disk r-3 cos θ. your first attempt you might get zero. Think about why and then tweak your integral....
Evaluate the surface integral. (x + y + z) ds, S is the parallelogram with parametric equations x = u + v, y = u – v, z = 1 + 2u + v, Osus 6, 0 SV 53. Is
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