/| 2rdV, where E is the region under the plane 2r + 3y + z = 6 that lies in the first octant as shown below; (7) Evaluate by converting to cylindrical polar coordinates E

Q: When transforming the triple integral a-st-y" (xZ+ y² + z²)ể dzdydx . 9-x2 9-X 2n n 3 to spherical…

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Q: 5. Evaluate the integral (z²² + y² + z²)³/²dzdydx by changing rectangular coordinates to spherical…

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Q: 9-y Consider the double integralf, dxdy. By converting to polar coordinates, the limits of…

A: We have to find the integration of limits for by converting the given integral into the polar…

Q: 1: Describe the solid bounded by the sphere ² +y² + z² = 9 and the pla 2 over the xy-plane using %3D…

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Q: 14. Find the double integral RV10-22-²dA by changing it to polar coordinates, where R is the region…

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Q: Q.3 (a) Express j= 3yî + x²j – x²k in terms of cylindrical coordinates. %3D - (b) Transform g = 2f…

A: Vectors are defined in Cylindrical  coordinates by (ρ, ϕ, z), where ρ is the length of the vector…

Q: 5. Use polar coordinates to find the volume of the solid enclosed by the hyper- boloid –r² – y² + z²…

A: To obtain the limits of integration for z, rewrite the equation -x2-y2+z2=1, and find z.…

Q: Q.3 (a) Express j = 3yî + x²j – x²k in terms of cylindrical coordinates. %3D (b) Transform g = ½f…

A: Since you have posted multiple questions but according to guidelines we will solve first question…

Q: can u help me with this Jacobian question please

A: Given transformation is

Q: 5) Consider the surface S shown in the graph, whose parametrization is given by by: r(u, v) = (v²,…

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Q: 4. Use cylindrical coordinates to evaluate [!] √²³² + y²dv₁ D where D is the region that lies inside…

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Q: Change to polar integral e-(z²+y*) dydx -1 1 -y1-z² o s: So re *drde drde re o f re *drde drde

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Q: #2. Use polar coordinates to find the volume of the solid bounded by the plane z = 0 and the…

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Q: Consider the double integralf", * dydx. By converting to polar coordinates, the limits of…

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Q: Sketch the region of integration and evaluate by changing to polar coordinates. P3/26 N²(x²+y² )dydx…

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Q: iii) Confirm your total flux calculation by computing the surface integral 2 > - #f. x-nds - Σ //₂²…

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Q: Find by using polar coordinates in R^2 the volume of the region bounded by the parabolic z=…

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Q: 1. Find the moment of inertial of the rectangular area of Figure 1.0 about the centroidal x and y…

A: we only solve one problem at a time so please submit them one by one.

Q: 1+√/1-4y² 1-√√/1-4y² _1 = ƒ/³ f²+ √² √²/ y dx dy.

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Q: 1 Change the double integral J. dydx into polar integral. 4-x² x² + drde drd0 drde 2[-drde or

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Q: Let D be the region enclosed by the surfaces z =-/4-x² - y and x² +y* . Determine JI| zdv by using…

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Q: change the iterated integrals to cylindrical coordinates 9-z²-y z ydzdydr -3 9-z2

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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: Consider the double integral dydx. By converting to polar coordinates, the limits of integration of…

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Q: (a) Let D be the region enclosed by the surfaces z =- |4–x² – y² and z= +y² . Determine zdv by using…

A: Triple integral is used to integrate the function of three variable over the three-dimensional…

Q: Compute the shared mass between the polar curves (r 2a cose) and (T = 2a sine) use density equal to…

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Q: Convert 18-22-y2 22 +y? +z dz dz dy into spherical coordinates. Hence evaluate the integral.

A: The volume of a solid can be calculated using the triple integrals in the spherical coordinates. The…

Q: Convert en extay?) JA O ver the region Q4. polar form and e to e Valuate let y= 7sino dA = rdrdo How…

A: ∫02π∫1e 2ln(r)(dr)(dθ) here we apply the ∫u*vdx rule ∫u*vdx = u∫vdx - ∫du/dx∫vdxdx so here 2lnr u =…

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

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Q: 2/ Find the line integrals of the ellipse+3= ellipse by x = acos(t) ,y= bsin(t) 1 , parameterize the…

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Q: 4. Find the area of the plane z 3r + 4y for all (r, y) eR where R is the region in the first…

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Q: Consider the double integralJ dydx. By converting to polar coordinates, 3 the limits of integration…

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Q: 4-y 1 Change the double integral dx dy into polar integra 5+ Vx? +y?

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Q: When transforming the triple integral 9-メ-y (xig'n 2') odzdydx -3 to spherical Coordinates becomes…

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Q: When transforming the triple integral 9-x 9-x2-y- (x² +y² +z?)% dzdydx 2n n 3 to spherical…

A: Triple integral conversion to special coordinates

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

A: Solution

Q: at Va:-x dz dy.dx

A: To convert the integral  ∫-aa∫-a2-x2a2-x2∫aa+a2-x2-y2zdzdydx to spherical and cylindrical…

Q: 4-z2-y2 By using spherical coordinates, evaluate the integral a dz dy dr

A: Consider the integral ∫01∫−1−x20∫04−x2−y2xdzdydx We have to evaluate the given integral by using…

Q: Calculate the line integral f(-102 + 4z + 5) de + (-7z – Oy? – by – 4) dy, where Dis the annulus…

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Q: Calculate the volume of the object resulting from the rotation of the region marked by the polar…

A: Given the equation of the curve in polar form as r=f(θ) where θ varies from θ1 to θ2 the volume of…

Q: 2. Let W be the portion below the plane z = centered at the origin in R3. Give a domain for…

A: We will use relation between cartesian and spherical co ordinate to find domain of W

Q: When transforming the triple integral 9-x2 9-x2-y2 (x²+ y² + z²)% dzdydx 2n n 3 to spherical…

A: The formula for the conversion of triple cartesian to triple polar coordinate is…

Q: #4. Use cylindrical coordinates to evaluate the integral 4-x2 7 3+2x2 + 2y2 dz dy dx

A: Evaluate the integral using cylindrical coordinates

Q: xy dA RVX² + y² a.) from Cartesian coordinates to polar coor- dinates where the region R is given on…

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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: Use cylindrical coordinates. Evaluate the triple intergral   5(x3 + xy2) dV, where E is the solid…

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Q: 5. Use polar coordinates to combine the sum NZ p* xy dydx + S 4-x2 L*y dydx + L,* xy dydx + La** xy…

A: Given: ∫121∫1-x2xxy dydx +∫12∫0xxy dy dx+∫22∫04-x2xy dy dx

Q: (9) Evaluate by converting to cylindrical polar coordinates 322dV where E is the solid bounded by y…

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Q: Consider the double integralf, 9-x2 dydx. By converting to polar coordinates, the limits of…

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Q: 9. Describe the region bounded by the lines y = r, y = -z and z = 2 in polar equations.

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