Find a parametric representation for the part of the cylinder y2 + z² = 36 that lies between the planes x = 0 and x = 4. %3D X = u y = 6cos(v) z = OsVS 2n Sus

Q: /| 2rdV, where E is the region under the plane 2r + 3y + z = 6 that lies in the first octant as…

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Q: SSL. xy dV, where T is the first-octant solid bounded by the coordinate planes and the upper half of…

A: Here we have to find  ∫ ∫ ∫T xy dV , where T is the first-octant solid bounded by the coordinate…

Q: Use polar coordinates to find the volume of the given solid. The solid above the xy-plane that lies…

A: Consider the given: It is the top of half circle if radius 1 in xy plane as its base.…

Q: Evaluate the unoriented line integral (22 + y° + z²) ds (2x² along the parametric curve a : [0, 1]…

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Q: Let S be the solid obtained by rotating the region shown in the figure about the y-axis. (Assume a =…

A: Consider given expression is, y=asin(bx2) Then, y=12sin(4x2) The given value of x=0 and x=πb that is…

Q: 1. Let E be the solid under the paraboloid 2=r'+y. above the ry-plane, and inside the cylinder +y =…

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Q: Sketch the indicated region D and integrate f(x, y) over D using polar coordinates. = V x2 + y2, D:…

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Q: Find the v o l um e generated by rotating the region bounded by the curves y = ex, x = 0, y = pi abo…

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Q: x(t) cos(t), y(t) = 1+ sin(t), with 0 < t < 2n

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Q: find a parametrization of the surface Circular cylinder band The portion of the cylinder y2 +(z -…

A: Given:The portion of the cylinder y2+(z-5)2=25 between the planes x=0 and x=10.

Q: Which of the following is the surface area of the surface generated by revolving the curve y = in…

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Q: (5) Use Stokes' Theorem to find the line integral |(* + 2y°)i + (y + z°) +(= + 2r*)k) • dř where C…

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Q: Consider the surface S shown in the gure and whose parameterization is given by: r(u, v) = (sin v,…

A: Consider the surface S shown in the gure and whose parameterization isgiven by: r(u, v) = (sin v, u…

Q: 19. Find the z coordinate of the center of mass of the wire represented by the parametric equations…

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Q: Find the length of the parametric x = e*, y = e=t, z = /2t, where 0 <t<1. ||

A: Given: x=et, y=e-t, z=2t  where 0≤t≤1

Q: Compute the volume of the solid below 2 – a? – y? and above the region D in the xy-plane. The…

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Q: Evaluate the surface integral. y ds S is the part of the paraboloid y = x² + z² that lies inside the…

A: The projection of S onto the xz-plane is the disk D=x,z: x2+z2≤9. We have to calculate the surface…

Q: ffff dydadz, where A is the region of hemisphere A ² + y² +2²=a²is the same as tripple integral by…

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Q: Give the integral representing the length of the parametric curve x=t^3, y=t^4, 0≤t≤1.

A: Given: A parametric curve:   Now the length of the parametric curve is given by the formula:

Q: Compute the volume of the solid below 2 – a? – y² and above the region D in the xy-plane. The…

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Q: Let E be the solid region in the first octant bounded by the coordinate planes, the cylinder…

A: The cylinder x2+y2=5y and the sphere x2+y2+z2=25. Obtain the triple integral: ∫∫∫Ey dV The solid is

Q: 'Use Cartesian coordinates to evaluate III y² dV where D is the tetrahedron in the first octant…

A: We have to use Cartesian coordinates to evaluate Volume where D is the tetrahedron in the first…

Q: Find an integral for the area of the surface generated by revolving the parametric curve about the…

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Q: Which of the following is the double polar integral that gives the volume of the solid surrounded by…

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Q: 7) Use cylindrical coordinates to evaluate (i) + yšav, where E is the region that lies inside the…

A: To evaluate the integral: Where E is the region that lies inside the cylinder, And between the…

Q: 17. Let T be the solid bounded below by the half-cone z = Vx² + y? and above by the spherical…

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Q: Evaluate the surface integral. (x + y + z) dS, S is the parallelogram with parametric equations x =…

A: Consider the given surface integral, ∬Sx+y+zdS Substitute the values x=u+v, y=u-v, and z=1+2u+v in…

Q: Given the triple integral r1 (2+r r3dzdrd0 o J3r2 1. Draw the given solid and its projection onto…

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Q: x = tsin (4t), y = tcos (4t), 0 ≤ t ≤ π / 2, which is the surface area integral of the body formed…

A: The volume of the body by revolving around the x-axis in the parametric form is given as So only B,…

Q: 5. Use spherical coordinates to evaluate the triple integral ///+y²+²dV, where E is the ball: x? +y?…

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Q: Use polar coordinates to evaluate the double integral V1 1-z2 dy dæ. (1+z² + y?)²

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Q: When transforming the triple integral V9-x2 (x2+y2 +z?) dzdvdx 2n n 3 to spherical coordinates…

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Q: Let S be the solid obtained by rotating the region shown in the figure about the y-axis. (Assume a =…

A: Given data: *The graph is f(x)=y=asin(bx2). *The value of the constant a and b is a=8 and b=4. *The…

Q: Consider the solid D that lies inside the cone z = and bounded by the spheres 3 y رد جر+ e][] p = 2…

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Q: t) Use spherical coordinates to evaluate the triple integral e-(2+y2+:?) AP E Vx2+y? + z2 E is the…

A: Here we evaluate the triple integral.

Q: Make a switch to cylindrical coordinates to evaluate V² + ² dV , where E is the region inside the…

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Q: Find the volume of the solid bounded by the plane z = 0 and the paraboloid z = 9 - x2 - y2. SOLUTION…

A: Solution

Q: Use Cartesian coordinates to evaluate y² dV where D is the tetrahedron in the first octant bounded…

A: Let us consider a triple integral of the form ∫ab∫f(x)g(x)∫h(x,y)r(x,y)F(x,y)dzdydx To solve the…

Q: Use cylindrical coordinates. Evaluate 3(x3 + xy2) dV, where E is the solid in the first octant that…

A: Given: The solid E is in first octant that lies beneath the paraboloid z=1-x2-y2.

Q: Let D be the solid region that lies above the cone z = x² + y² and below the sphere x+y²+= = =. The…

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Q: Use cylindrical coordinates. Evaluate (x + y + z) dV, where E is the solid in the first octant that…

A: We need to find , triple integral  ∫∫∫E x + y +z dV  where E is the solid in the first octant that…

Q: 7. Use spherical coordinates to find ||| z dx dy dz where E is the solid defined by E Os Vr* +y³ <z…

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Q: 2)use the polar coordinates to evaluate the double integral: )x2 +y2 dA R is the disk x2 + y2 < 9 A)

A: We have to use polar coordinates here.

Q: S Find the voleime of the solid generated by revolving the region baunded by the given lines Cnd…

A: Hint: Try Disk Method to find the volume.

Q: (10) Sketch the solid bounded by z = x2 + y? and z 4- x2 - y². Use cylindrical coordinates to find…

A: Given ∫∫∫Dx2+y2dVand solid bounded by z=x2+y2 and z=4-x2-y2

Q: Use cylindrical coordinates. Evaluate |I| 3(x3 + xy2) dV, where E is the solid in the first octant…

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Q: Use spherical coordinates to evaluate the triple integral e-(x² + y² +2²) J dV, x √2² + y² + 2² E…

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Q: The area of the surface obtained by rotating the curve y = et +e asxsb, about the x-axis is 1/2 e2 +…

A: Find the surface area rotating the curve about x axis