A solid G is bounded by the paraboloid z = 4 - x? – y?, the cylinder x² + y? = 4 and the plane z = 5. Evaluate r + y+2:) dV. G

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

A:

Q: Given: ZWZX ZYZX; ZW = ZY Prove: ZX is a perpendicular bisector of WY

A:

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

A:

Q: Let S be the solid bounded by the planes z = o and y + z = 3, and the cylinder x2+y2 =2y-

A: answer is in next step

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

A:

Q: Find the area of the part of the plane  z = ax + by + c  that projects onto a region in the…

A:

Q: Compute the distance d from y to the plane in R' spanned by u1 and uz.

A: We have to find the distance d from y to the plane in R^3.

Q: Evaluate e dV where E is enclosed by the paraboloid z = 4+ x² + y?, the cylinder E x2 + y? = 1, and…

A:

Q: Consider the solid that is bounded above by x² + y? + z? = 169 and below by z=5. %3D

A: In this question, we have to write the triple integral to find the volume of the solid bounded by…

Q: Evaluate e dV where E is enclosed by the paraboloid z = 2 + x² + y°, the cylinder z² + y² = 2, and…

A:

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

A:

Q: Consider the surface S: z = 4 - x2 ,bounded by y = −5(x2 - 1) and y = 0, just as it is shown in the…

A: We have to find the area of the surface S, and we will use surface integral to do that.

Q: Without using the formula (Gauss), calculate S=∂E∫F(x).n(x)ds, where F(x) = x32k ,E : x12 + x22≤ x3,…

A: Typing the equation may be some mistake. 0≤x3≤1 and another 0≤x3≤11, first one i accept.

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

A:

Q: Evaluate /// 203 dV G if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: Here we have to find range of values for x,y and z and then find triple integral

Q: If F = 2y i - zj + x²k and S is the surface of the parabolic cylinder y²= &x in the first octant…

A:

Q: Let C be the positively oriented square with vertices 0, 1, 1 + i, i. Evaluate using the definition…

A:

Q: Evaluate the triple integral ///. zdV, where E 4. is bounded by the cylinder y2 + z? = 4 and the…

A: According to the given information, it is required to evaluate the triple integral.

Q: Evaluate e dV where E is enclosed by the paraboloid z = 5 + x² + y°, the cylinder 2² + y? = 5, and…

A:

Q: Evaluate where G is the solid in the first octant bounded by paraboloid : = + y, the cylinder r+ y 9…

A:

Q: Use the Divergence Theorem to evaluate (4x + 9y + z2) ds where S is the sphere x2 + y2 + z? = 1.

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: If F = xy?i + yz? j + zx2k, and S is the region bounded by the triangle with vertices (1,0,0),…

A:

Q: Use the Divergence Theorem to evaluate (6x + 7y + z2) dS where S is the sphere x2 + y2 + z? = 1.

A:

Q: CALCULATE S SS F(x, y, z)dxdydz WHERE: T f(x, y, z) = x AND "T" IS THE SOLID DELIMITED BY THE…

A:

Q: Evaluate dV, where E lies between the spheres x + y² + z? = 16 and E x2 + y2 + z2 r + y + z 64 in…

A: Follow 2nd ,3rd step .

Q: 7. Let E be the region in R enclosed by the cone z = Va2 + y? and the paraboloid z = a2 + y?. Then…

A:

Q: Evaluate SSS z²dV, where R is the region given R by above the plane z=O and between the spheres 2. +…

A: A scalar function is a rule that is used to associate a number, or quantity with a particular point…

Q: Evaluate zdV where E is the region under the plane 4x + 2y + z = 4 in the first octant ( E х, у, z >…

A:

Q: Evaluate e dV where E is enclosed by the paraboloid z = 5 + x² + y°, the cylinder 2² + y? 1, and the…

A:

Q: Given that the total flux across the surface, S of the tetrahedron bounded by the planes x= 0, y=0,…

A: Given Vector field is F = 2xi + 3yj - zk

Q: Calculate ( (2x + y) dV , where V is a closed space bounded by the cylinder z = 4 – x? and the…

A:

Q: A solid G is bounded by the paraboloid z = 4 – x2 – y?, the cylinder x2 + y? = 4 and the plane z =…

A:

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

A:

Q: Evaluate e dV where E is enclosed by the paraboloid z = 2 + x² + y², the cylinder æ? + y² = 5, and…

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: Given that the total flux across the surface, S of the tetrahedron bounded by the planes x=0, y=0.…

A: To draw graphs in 3d we need to find intersections with co ordinate axes and also with co ordinate…

Q: Evaluate e dV where E is enclosed by the paraboloid z = 4+x² + y°, the cylinder x² + y? = 3, and the…

A: Here we have to evaluate ∫∫∫E ez dV , where E is the enclosed by the paraboloid z=4+x2+y2 , the…

Q: A: Determine the mass and center of mass of the solid that bounded by the paraboloid z = 9y? + 9x?…

A:

Q: Let S denote the part of the cylinder x2 + y² = 9 that lies between the planes r + y = 1 and x – y =…

A:

Q: Given that o is the part of the surface z = 4 – x in

A: Given, the surface z = 4 - x in the first octant from y = 0  to  y = 2. If ψx, y, z=xyz, F(x, y, z)…

Q: Evaluate e dV where E is enclosed by the paraboloid z = 4 + x² + y², the %3D cylinder x? + y² = 3,…

A: We need to evaluate integral.

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 bounded by surfaces S1, S2, S3, S4, S5, and S6 with vertices A, B, C, D, E and O,…

A: In this question, we use the given sketch of the surface and find the parametrization for each…

Q: Evaluate e dV where E is enclosed by the paraboloid z = 1+ æ² + y°, the cylinder a? + y? = 4, and…

A:

Q: se the Divergence Theorem to evaluate (8x + 12y + z2) ds Is here S is the sphere x2 + y2 + z² = 1.

A: To compute the below integral using divergence theorem.

Q: Evaluate || 4.nds , where A=zi+xj – 3y°zk and S is the surface of the cylinder x² + y =4 included in…

A: Let ∅=x2+y2-4  Then the normal to the surface S is ∇∅=2xi+2yj The unit normal is…

Q: Evaluate e dV where E is enclosed by the paraboloid z = 5 + x? + y?, the cylinder x? + y? 5, and the…

A:

Q: Evaluate e dV where E is enclosed by the paraboloid z = 5 + x + y°, the cylinder + y = 1, and the ry…

A: To Determine: evaluate ∫∫∫eZdV  where E is enclosed by the paraboloid z=5+x2+y2,the cylinder…

Q: Evaluate the following double integral dydr, -here D is the entire plane

A: The question is taken from the calculus in which we have to find the double integral of given…