1. Find the area of the part of the planer+ 2u + 3z = 1 that lies inside the cylinder x2 + y? = 3.

Q: Find the area of the surface. The part of the paraboloid x = y? + z² that lies inside the cylinder…

A: We have to find the surface area according to given information

Q: The value of the triple integral 22 zdV where E is the upper E half of the sphere of x² + y? + z? =…

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Q: 3. Find the surface area of the surface created when the cylinder y + 2- intersects the cylinder 1²…

A: surface area of the surface given by equation z=f(x,y) A=∫∫Dfx2+fy2+1dA D is the region on xy plane

Q: Find the surface area of the part of the plane 4+ 2x + 3y that lies inside the cylinder x² + y? 9.

A: The area is given by using double integral

Q: Compute the area of the portion of the cone x2 +y = z2 with z z 0 that is inside the sphere x y z…

A: Given the area of the cone is x2+y2 = z2 and the sphere is x2+y2+z2 = 2Rz.

Q: Let S be the part of the hyperbolic paraboloid z = x2- y2 located between the cylinders x2 + y? = 1…

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Q: 1 Find the area of the surface obtained by rotating the curve y = In(1 – x²), 0 < x <. about the

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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: 1. Find by integration the area of the surface of revolution generated by revolving the loop about…

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Q: ind the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 - x2 + 4 and above the…

A: Using the double integral formula.

Q: Compute 3xy dS, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

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Q: Prove that the integral of the bottom of a half ellipsoid, (x/a)^2 + (y/b)^2 + (z/c)^2 =1, is equal…

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Q: 3. Find the volume of the solid that lies between the paraboloid z = x² + y² and the sphere x2 + y²…

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Q: 1. Find the area of the portion of the plane Зх — Зу + 2 — 12 that lies inside the cylinder y? + 22…

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Q: Use SphericalL coerdinates to evaluate the +र |राज्ट | . triple integral SSS x°*y@;=? d V, Where E…

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Q: 2. Find the area of the part of the surface z = cylinder x2 + y² = 9. 3xy that lies within the

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Q: Use Greens Theorem to evalua te the line integral Sr -93 dx +x*dy. where C is the positively onented…

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Q: find volume 26. The wedge cut from the cylinder x2 + y? = 1 by the planes z = -y and z = 0

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Q: (1) Find the area of the surface of the portion of the cone 2 +y² between the cylinder y? = x and…

A: To find the surface area of cone between given cylinder and plane, use the surface area formula as…

Q: * Find the surface area of the part of the plane 2x + 5y + z = 2 that lies inside the cylinder x? +…

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Q: 8. Find the surface area of the part of the sphere x2 + y? + 22 : = 4z that lies inside the…

A: The solution is given as

Q: Find the surface area of the part of the circular paraboloid z = x + y that lies inside the cylinder…

A: Solve the given

Q: Find the value(s) of c such that the area of the region bounded by the parabolae y=x^2 - c^2 and…

A: Given: The given parabolas are y=x2-c2 and y=c2-x2. Determine the points of intersection.…

Q: Consider the solid whose base is the region bounded by 4x? + 9y? = 36. Y 3 -3 -2 -1 -1 2 3 2 -3 1.

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Q: Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2…

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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 region endlased R by the cunes V=12-2y +1 and Y= -2+2x ャ4.

A: Answer

Q: Find the surface area of the portion of the surface z = xy which is inside the cylinder p2 +3? = 9.

A: It is given that the portion of the surface is z=xy=fx,y. The surface area of the surface is…

Q: (a) Compute the area of the portion of the cone x2 + y2 = z? with z 2 0 that is inside the sphere x2…

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Q: 10. Find the area of the paraboloid x² + y + z² = 2 by the plane y = 0. (Hint: Implicit Surface)

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Q: Find the surface area of the part of the hyperbolic paraboloid z = y? –x² that lies between the…

A: Given The hyperboloid z=y2-x2 that lies between the cylinders x2+y2=1 and x2+y2=4.

Q: 3. Find the exact area of the surface resulting from rotating y = v1 + e* from x = 0 to x = 1 about…

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Q: Calculate the surface area of the paraboloid with top radius R> 0 defined by 2 a² + y? 0< x² + y? <…

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Q: Evaluate the surface integral. JI (12 + y2 + 2) ds S is the part of the cylinder x2 + y2 = 9 that…

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Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 – x2 + 2 and above…

A: To find the volume of the solid that lies under the hyperbolic paraboloid  z=3y2-x2+2 and above the…

Q: An integral expression for the area of the surface generated by rotating the line segment joining…

A: Given that: Points are- (3,1) , (6, 2)

Q: Show that the volume of the segment cut from the paraboloid x2 /a2 + y2/ b2 = z/ c by the plane z =…

A: Show that the volume of the segment cut from the paraboloidX^2 /a^2 + y^2/ b^2 = z/ cby the plane z…

Q: The value of the line integral S(2xy²dx + 2a?ydy + dz) along a path joining the origin and the point…

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Q: Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2…

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Q: 4) The area of the surface generated by revolving x=y²-1, 1≤ y≤ 2 about x-axis is S=.

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Q: 5. Find the volume generated by the equation x2 +y² – 4x - 6y –- 12 = 0 if it is rotated about the…

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Q: Find the area of the part of the paraboloid x = y2 + z2 that lies inside the cylinder y2 + z2 = 1

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Q: 3. Find the area of the surface cut from the paraboloid x? + y +z = 2 by the plane y = 0.

A: Here we have to find the area of the surface cut from the paraboloid x2+y+z2=2 by the plane y=0.

Q: tes to evaluate the triple integral e Vz² + y² + pounded by the spheres z² + y² + z² = 4 and z? + y…

A: Given, ∫∫∫Ee-x2+y2+z2x2+y2+z2dV E is the region bounded by spheres x2+y2+z2=4 and x2+y2+z2=25.

Q: 1. Find So(r+2y)dA, where D is the region bounded by the parabolas y r, and y=1+

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Q: What is the value of the double integral 128(e – 1) e(42+8y)? dA, 2 R where Ris the triangular…

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Q: By using double integrals, find the surface area of plane + y² -+z=c that lies inside a a the…

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Q: 1) Find the volume of the solid that lies between the paraboloid z = 2x² + 2y² and the plane Z = 8.

A: The main objective is to find the volume of solid that lies between the paraboloid z=2x2+2y2 and the…