Compute 6. da dy dz x²+y² + z² where V = {(x, y, z) E R³ : 4 < x² + y² + z² < 9, z > 0, y > 0}. Sketch the solid.

Q: Find JJJ and 2 = y dV, where E is the solid bounded by the parabolic cylinder z = 15 - 4y Question…

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Q: Calculate F· dS where F = (3xy', ze", 2°) and S is the surface of the solid bounded by the cylinder…

A: We need to calculate ∬SF→.dS which is the flux. Now, we can use the divergence theorem to find…

Q: 1 in 1in y 1 in 3 in 1 in X

A: Consider the diagram and divide into four regions as shown below, Now, make a chart and evaluate…

Q: p) Classify the following models as ARIMA(p,d,q). i) (1-B)x, = (1-0.3B),. ii) (1-0.5B+0.25B²)Vx, =…

A: ARIMA means auto regressive integrated moving average, It ia also written in the forn ARIMA(p,d,q)

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

A: The volume of the solid generated by resolution can be calculated by calculating the surface area of…

Q: 2. Calculate the centroid of the thin plate R which bounded by a = 1, y = 0 and, x² + y² = 4.

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Q: The volume of the solid bounded by the plane 3x+6y-2z=12 and the coordinate planes is O A. 2-2y+4 1…

A: We need to find the volume of the solid bounded by the plane 3x+6y-2z=12. Now,…

Q: Evaluate . F dr where F(x,y,z) = (cos x, -2x, y + sin(z³)) and C is the boundary of the triangle…

A: This is a problem of surface integral.

Q: Consider the solid mmited by the following surfaces: S,: x=4-7 SziytZ=Z S3: 2xty+ z= 2 C) 2=2- 2z…

A: Here we find the projection of the solid on the xz-plane.

Q: Use Cartesian coordinates to evaluate [[[ ²² y² dv D where D is the tetrahedron in the first octant…

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Q: Evaluate /|/. x dV where E is the solid enclosed by the paraboloid x = y²+z² and the plane x = 9

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Q: Let S be the solid obtained by rotating the region bounded by C1: y = x2 − 6x + 9 = (x − 3)2 and C2:…

A: The given curves are y=x-32, and y=x+3. To Sketch: The region bounded by the above curves and which…

Q: 3 dx a) 3- x

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Use spherical coordinates to evaluate fff (9-x² - y2) dV where E is the solid hemisphere E x² + y2 +…

A: To Evaluate: The integral ∫∫∫E9-x2-y2dV where E: x2+y2+z2≤9 , z≥0 using spherical coordinate system.

Q: 5. Evaluate Sl. x2 dV where is the solid that lies within the cylinder x² + y² = 4 above the plane z…

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Q: Calculate F.ds where F = (3xy², xe², z³) S is the surface of the solid bounded by the cylinder y² +…

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

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Q: Evaluate 1 x² + y² + z² between the spheres x² + y² + 2² = 9 and x² + y² + z² = 36 in the first…

A: x=rsin⁡θcos⁡ϕ, y=rsin⁡θsin⁡ϕ, z=rcos⁡θFor the region E, 3≤r≤6, 0≤θ≤π/2,…

Q: Find SS₁² z dV, where E is the solid tetrahedron with vertices (0,0,0), (6,0,0), (0,1,0), and…

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Q: 2. Evaluate O (2y + In(5x² +3)) dx + (10x 3) dy along the boundary of the elliptic- region 4. y? 1…

A: Introduction: Green's theorem is very efficient in calculating line integral. When the line intgeral…

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

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Q: • SS,F. F = (4x³z, 4y³z, 3z¹) Calculate F.ds where and S is the surface of the solid bounded by the…

A: Given,                           F→=4x3z, 4y3z, 3z4, and S is the surface of the solid bounded by…

Q: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

A: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

Q: 4. Evaluate //F FdS, where F(x, y, z) = (2x + 2xz, -4xy², y - z2) and R R surface of the solid…

A: The given problem is to evaluate the given surface integral over the given solid surface bounded by…

Q: Evaluate f. F dS where F(x,y, z) = (4x³z, 4y³z, 3z*) and S is the surface of the solid bounded by…

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Q: FIND THE DIVERGENCE AND CURL OF U = i (x 2+ yz)+j Cy?+Zx) t K (z?+xy] %3D

A: Given :u=i x2+yz+jy2+zx+kz2+xy.We need to find the divergence and curl of u.