Find the area of the portion of the cylindrical surface y = 4 – x² in the first octant that is between the xy-plane and the surface x2 + 2x + y - z = 4.

Q: Find the volume of the solid that lies under the plane 4x + 8y − 2z + 13 = 0 and above the rectangle…

A: Find the volume of the solid that lies under the plane 4x + 8y − 2z + 13 = 0 and above the rectangle…

Q: Determine the surface area of the solid obtained by rotating y = V(2p – x)(2p + x), |x | < 2 about…

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Q: Use cylindrical coordinates to evaluate the triple integral ||| E is the solid bounded by the…

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Q: Use cylindrical coordinates to find the volume of the solid. Solid bounded by the graphs of the…

A: Given that, The solid bounded by the graphs of a sphere r2+z2=49   and r =7 cosθ We have to find…

Q: Evaluate the surface integral. xz ds, S is the part of the plane 2x + 2y + z = 4 that lies in the…

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Q: Evaluate the surface integral. ) ر م(ل 2) ds S is the part of the cylinder x² + y2 = 16 that lies…

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Q: Find the volume of the solid whose base is the triangle in the xy-plane bounded by the x-axis, the…

A: Given plane z=3-x-y and the lines y=x and x=1. The objective is to find the volume of the solid…

Q: Find the area of the portion of the cylindrical surface Y = 4 – x² in the first octant that is…

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Q: Use cylindrical coordinates to find the volume of the solid bounded by the paraboloid of revolution…

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Q: The solid in the first octant bounded by the coordinate planes and the plane z = 8 – x – y dz dy dx

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Q: Find the average height of the hemispherical surface z = sqrt(a2 - x2 - y2 )above the disk x2 + y2…

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Q: Use cylindrical coordinates to evaluate the integral 2²dV where E is the solid that lies within the…

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Q: Evaluate the surface integral. || x²yz ds, s is the part of the plane z = 1 + 2x + 3y that lies…

A: To find ∬Sx2yz dS Here 0≤x≤5  and 0≤y≤2 S→=xi→+ yj→+…

Q: Find the vo lume oF the solid OF revolution when the regiON bounded by y = x +1, the solid X-axis,…

A: Given problem:- Find the volume of the solid of revolution when the region bounded by y = x + 1 the…

Q: Find the polar moment of inertia about the origin of a thin triangular plate of constant density d =…

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Q: Find the surface area of the part of the plane 2x+2y +z=4 that lies inside the cylinder x²+y² = 2.…

A: Given that, the equation of the plane is 2x+2y+z=4 and the equation of the cylinder x2+y2=2. Note…

Q: Evaluate the surface integral. /| x*yz ds, s is the part of the plane z=1+ 2x + 3y that lies above…

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Q: Find the volume of the solid under the plane 3x + 2y – z = 0 and above the region enclosed by the…

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Q: Evaluate the surface integral  ffR(x+y)dS where σ is the portion of the plane z = 6 − 2x − 3y in the…

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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: Find the surface area of that part of the plane 9x + 6y + z = 4 that lies inside the elliptic…

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Q: Use cylindrical coordinates to evaluate the triple integral ∫∫∫E √(x2+y2)dV, where E is the solid…

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Q: Evaluate the surface integral. /| xz ds, S is the part of the plane 2x + 2y + z= 4 that lies in the…

A: We need to find surface integral.

Q: Find the surface area of the portion of the surface x2- 2 In a+ V15 y - z = 0 above the rectangle 1…

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Q: Evaluate the surface integral. J[x²³x² x²yz ds, S is the part of the plane z = 1 + 2x + 3y that lies…

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Q: . Find the area of the surface obtained by rotating y = S, Vs² – 1 ds, 1 < x < 2 about the y-axis.

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Q: Use cylindrical coordinates to evaluate the triple integral |||| Væ² +y² dV, where E is the solid…

A: Mentioned below is the answer

Q: Find the volume of the solid that lies under the plane 4x + 6y – 2z + 17 = 0 and above the rectangle…

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Q: nd the volume of the solid bounded by the paraboloid z = 32 – x² – y², the cylinder r² + y? = 16 and…

A: The solution are next step

Q: Q4 (a) Calculate the surface integral: [] (² + (y² + 2yz) dS where o is the first octant of the…

A: To evaluate the surface integral Given plane 2x+y+2z=6

Q: 3. Find the volume under the paraboloid 3z = 2.12 + 2y2, above the triangle enclosed by the lines y…

A: First we have to draw graph and find limit according to which we have taken strip along y . Find…

Q: Find the surface area of the paraboloid z =1-x² - y? that is above the xy-plane.

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Q: Find the surface area of the cone z = x² + y2 that lies between the plane y = x and the cylinder y =…

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Q: calculate the surface area of the solid obtained by rotating the curve over the g.iven interval…

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Q: Find the volume of the solid that lies under the plane 4x + 10y – 2z + 19 = 0 and above the…

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Q: Find the volume of the solid that lies under the surface z = 4 +y and above the region D in the…

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Q: Determine the element of surface area dS in the special case of the paraboloid of revolution z = x2…

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Q: The solid in the first octant bounded by the coordinate planes and the plane z = 3 – x –y dz dy dx

A: Answer is:∫03∫03-x∫03-x-ydzdydx Proof is attached below.

Q: Find the surface area of the cone z = ' + y² that lies between the plane y = x and the cylinder y =…

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Q: The region cut from the solid elliptical cylinder x2 + 4y2≤ 4 by the xy-plane and the plane z = x +…

A: Given that, z=x+2 , x2+y2≤4

Q: Find the volume of the solid that lies under the plane 4x + 10y - 2z + 15 = 0 and above the…

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Q: Evaluate the surface integral (4x² + 3y)dS where S is the part of the plane 2.x + 5y + z = 48 inside…

A: We need to calculate:∬S4x2+3ydS over the surface S,which is the part of plane 2x+5y+z=48, inside the…

Q: Find the volume of the solid bounded by the elliptic paraboloid z = 5 + 4a² + 3y?, the planes a and…

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Q: Let S be the part of the cylindrical surface x2 + y2 = 4 limited by the plans z = 0 and z = y + 2.…

A: Let S be the part of cylindrical surface x2+y2=4, limited by z=0 and z=y+2 The formula to find the…

Q: Find the surface area of the portion of the cone z = x2 + y2 in between the planes z = 3 and z = 4.

A: The area of the surface z=fx,y above a region R of the xy-plane is given as follows.…

Q: need ASAP B. Find the area of the portion of the cylindrical surface y = 4 − x2 in the first…

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Q: Find the surface area of z =1-(x^2)-(y^2) that is above the xy plane

A: Given equation of plane is  z=f(x,y)=1-x2-y2 we have to find the surface area above xy plane.

Q: Evaluate the surface integral. || x2yz ds, s is the part of the plane z = 1+ 2x + 3y that lies above…

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