6. Consider the triple integral: zdv, -x2 – y?, from above by the paraboloid where V is the region bounded from below by the cone z = z2 = 2(x² + y²) + 4 and inside the cylinder x2 + y² = 1. Sketch the region. Use the cylindrical polar coordinate (r, 0, z) to evaluate the integral.

Q: Calculate F· dS where F = (4x*z, 4y°z, 3:*) S is the surface of the solid bounded by the hemispheres…

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

A:

Q: luate the surface integral. // (x + y + z) ds, S is the parallelogram with parametric equations x =…

A: Sub x= u+v  y= u-v  z= 1+2u+v

Q: Use spherical coordinates to evaluate the triple integral e-(z²+z²+z²) / x² + y² + z² where E is the…

A:

Q: Consider the curve C between the points (1,0, 1) and (0, 1, 1) at the intersection of the cylinder…

A: To evaluate the line integral along with the curve c of ω=−ydx+xdy+dz.

Q: Evaluate the iterated integral ㅇ 푸corl ㅇ 플 ○ Cor2 0 1 cos(x+y)dy dx by converting to polar…

A:

Q: Evaluate the surface integral. y dS, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

A: Consider the provided question,

Q: Consider the polar curves C₁: r: = 3 (blue) and C₂:r = 2 − 2sin0 (red) and let R be the shaded…

A:

Q: (9) Evaluate the surface integral / S, czdS, where o is the part of the plane r+2y+3z = 6 that lies…

A:

Q: The region R is the interior of the tilted ellipse given by x ry + y = 2, shown below. Sketch the…

A:

Q: Use spherical coordinates to evaluate the triple integral x² + y² + z² ≤ 64. 11. 2² + y² + 2² dV,…

A:

Q: Evaluate ∫ ∫ √ (x2+ y2) dA where R is the portion of the annulus 1 ≤ x2 + y2 ≤ 16 with y ≤ 0 using…

A: We have to evaluate the double integral.

Q: Find the area of the surface. T'part of the paraboloid x = y² + z² that lies inside the cylinder y²…

A:

Q: 2. Evaluate the integral by first converting into spherical coordinates: |4–x² 4-x² J2-. r2+/4-x²-y²…

A: The objective is to convert the integral to spherical coordinates and evaluate it,…

Q: Find the volume of the solid within the cylinder (x - 1)2 + y2 = 4 bounded by y + z = 4 and z = 0…

A:

Q: Calculate the double integral ∬Rsin√x2+y2dxdy by transforming to polar coordinates. The region R is…

A:

Q: Evaluate the triple integral z dV, where E is enclosed by the paraboloid z= 4x2 + 4y2 and the plane…

A:

Q: (x + y + z) ds, S is the parallelogram with parametric equations x = u + v, y = U-v, z = 1+2u+v, 0 ≤…

A:

Q: 4. Use polar coordinates to find the volume of the solid that lies under the paraboloid: z = x² +…

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Q: Find the double integral SSR V10-2²-y² dA by changing it to polar coordinates, where R is the region…

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Q: P): Evaluate the double integral y dA, where R = ((x, y)| x² + y 2 4, x² + y < 9, y 2 0} by using…

A:

Q: Use spherical coordinates to evaluate the triple integral SSSE x2 + y2 + z2 dV, Where E is the ball:…

A: Use spherical coordinates to evaluate the triple integral SSSE x2 + y2 + z2 dV, Where E is the ball:…