=+ x²y) ds part of the cylinder y² + z² = 9 that lies between the planes x = 0 and x = 3 in the first octant

Q: 7) z dV, E is the solid enclosed by the cylinder r2 +y = 1, and the E planes z = 0 and z 3.

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Q: Use Cartesian coordinates to evaluate JIJ y² dv 2 D where D is the tetrahedron in the first octant…

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Q: z dv, where E is enclosed by the paraboloid z = x2 + y² and the plane z = 4. Evaluate

A: see 2nd step

Q: y dV, where B is the portion of the unit ball B = {(x, y, z) : x² +y² + z² < 1} which lies below the…

A:

Q: Find fff y av, y dV, where E is the solid bounded by the parabolic cylinder z = ² and the planes y =…

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

A:

Q: Evaluate f, A.n ds, where A = zi +j- 3y²zk and S is the surface of cylinder x? + y? = 16 included in…

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Q: The simple solid Q, drawn in the first octant and generated by the surfaces y – 1 = (x – 2)² | 3x +…

A: We have to draw the solid Q in first octant and is generated by the surfaces  y- 1=( x- 2)2 3x+2z=11…

Q: Below is the solid Q bounded by the surfaces S,: x? +y? +z? = 4, S;: z = V3 and S,: y= x in the…

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Q: Use Stokes' Theorem to caleulate ſ. F - dř, where F = zyi+3=3+5zk, and C is the closed path around a…

A:

Q: a) Evaluate (-ri-yj+2z k) n dS, where a is the portion of the paraboloid : 3x +3y between the planes…

A: We have to Evaluate the Integral using polar coordinate

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: Jff v² av where D is the tetrahedron in the first octant bounded by the coordinate planes and the…

A: Let us consider the given integral I=∫ab∫f(x)g(x)∫p(x,y)q(x,y)F(x,y,z)dzdydx To solve the triple…

Q: In which part of the (x, y) plane the following equation is elliptic? Uzr + 4ury + (x² + 4y*) uyy =…

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Q: Evaluate (Vx A). ndS over the surface of intersection of the cylinders x + y a, = a which is…

A:

Q: Considering f(x, y, z) = z + x²y and S as part of the cylinder y? + z² = 25 that is between the…

A: Given that, fx,y,z=z+x2y and S is the part of the cylinder y2+z2=25 that is between the planes x=0…

Q: Evaluate ez dV where E is enclosed by the paraboloid z = 4 + x? + y², the cylinder x? + y? = 1, and…

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Q: a) Find the points at which the twisted cubic F(t) = ti + t} +tk intersects the plane 4.x +2y+z = 24…

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Q: Which of the following represents the area of the surface cut from the plane z = ax + by by the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate y-dV, where E is the solid that lies within the cylinder x+y = 49, %3D above the plane z =…

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Q: Use Cartesian coordinates to evaluate Jff v² av . D where D is the tetrahedron in the first octant…

A: We need to find the integral , ∭D y2 dV   where D is the tetrahedron in the first octant bounded by…

Q: Calculate Se(5x + 3y) i + (4x + 3y) j) · dĩ where C is the circular path with center (a, b) and…

A:

Q: a) Evaluate [-ri-yj+2: k) - n ds, (-a i- where a is the portion of the paraboloid z = 3r + 3y…

A:

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

A:

Q: Evaluate z* + x dS where S is the cylinder x2 + y? = 36 between the planes z = -3 and z = 1,…

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Q: The simple solid Q, drawn in the first octant and generated by the surfaces y – 1 = (x – 2)² 3x + 2z…

A:

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

A:

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: Use Cartesian coordinates to evaluate JJ v² av where D is the tetrahedron in the first octant…

A:

Q: Integrate g(x, y, z) = x4y(y2 + z2 ) over the portion of the cylinder y2 + z2 = 25 that lies in the…

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Q: (b) Evaluate SSI, zdV, where D is the solid tetrahedron bounded by the four planes x = 0, y = 0,z =…

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Q: Find y dV, where E is the solid bounded by the parabolic cylinder z = = 2 and the planes y = 0 E and…

A: The solution is given below

Q: Integrate g(x,y,z) = x + 5y + z over the portion of the plane 4x + 8y + z = 8 that lies in the first…

A:

Q: O 9/ Compute I - [.lryz) , uhere s is the part g the plane y +x that lies inside the half-cylinder…

A: We know that, dS=1+∂z∂x2+∂z∂y2dydx where S is the part of plane z=y+x. ∂z∂x=1∂z∂y=1 dS=1+(1)2+(1)2…

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 8x + 16y + 24z on the elipse…

A: To determine the maxima and minima of the function f(x, y, z) with respect to the function is…

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 sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y+ 12z on the elipse…

A:

Q: Calculate fc((7x + 6y) i + (4x + 7y) j) dr where C is the circular path with center (a, b) and…

A: The path is given as the circular with center (a, b). Now the integral is: I=∫C (7x+6y)i→ +…

Q: Which of the following is the least distance from the origin to the plane 2x + 2y + z = 1? Lütfen…

A: We have to find

Q: a) Evaluate /| (-ri-yj+2: k) · n dS, where o is the portion of the paraboloid z = 3x2 + 3y? between…

A: Define a function fx,y=z or fx,y=3x2+3y2.  So, the flux integral is:…

Q: Consider the solid Q, in the first octant, which is generated by the surfaces: S1 : x2 = −(z − 3),…

A: Given:  S1 : x2 = −(z − 3), S2 : y + z = 3, S3 : z = 2, S4 : z = 0, S5 : y = 0 and S6 : x = 0  The…

Q: The distance from a point S(xo, Yo, Zo) to a plane M: ax + by + cz + d = 0 is given by In PS| d :…

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Q: a) Evaluate (-x i - yj+ 2z k) - n dS, where o is the portion of the paraboloid z = 3r2 + 3y? between…

A:

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

A:

Q: a) Evaluate //(-ri-yj+2: k) n dS, where a is the portion of the paraboloid : = 3r - 3y between the…

A:

Q: Use Cartesian coordinates to evaluate JJJ² dV D where D is the tetrahedron in the first octant…

A: Given ∭y2 dVD

Q: Use Cartesian coordinates to evaluate Jff v² av D where D is the tetrahedron in the first octant…

A: Let us consider the integartion I=∫ab∫f(x)g(x)∫p(x,y)q(x,y)F(x,y,z)dzdydx To solve the integral…

Q: yz ds where o is the part of the plane x + y+ z = 1 that lies in the first octant.

A: Given The given integral ∫∫σyzds over the region x+y+z=1 that lies in the first octant can evaluated…

Q: Evaluate +y² 1 Ez² + y² JJJ₁² dV, where E lies between the spheres z² + y² + 2² +2² 16 in the first…

A: Given that,

Q: Evaluate z dv, where E is enclosed by the paraboloid z = x² + y2 and the plane z = 16.

A: