Integrate the function (ಠ+ y²) ½ over the region E that is bounded by the xy plane below and above by the paraboloid 3 – x² - y² using cylindrical coordinates. where A = E = F The value of the integral is B = [1] E [[[₁₂ (2² + y²) i dv= E and G(z, r, 0) (x² + y²) ¾ dV = | B D -L²³L²T² C = D = [²G(z,r,0) dzdrdo

Q: Evaluate the surface integral. JS (x+y+z) dS, S is the parallelogram with parametric equations x = u…

A: We find the surface integral.

Q: Evaluate the line integral Jc F · dr, where F(x, y, z) = xi – yj + 3zk and C is given by the vector…

A: Given F(x,y,z)=xi-yj+3zk and C is the curve given by  rt=sint,cost,t. Find ∫CF·dr.

Q: Use the map G(u, v) = a = 4, b = 8, c = 6. b J D a y=cx uv v+1' v+1 (x + y) dx dy = to compute f (x…

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Q: C is the intersection curve between the paraboloid z=x²+y² and

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

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Q: Evaluate the surface integral. J[x (x + y + z) ds, S is the parallelogram with parametric equations…

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Q: Use cylindrical coordinates.Evaluate the integral, where E is enclosed by the paraboloid  z = 2 + x2…

A: Consider the integral which is to be evaluated:

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

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Q: Use cylindrical coordinates to evaluate the triple integral SSS √x² + y² dV, where E is the solid…

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Q: Evaluate the line integral ScF- dr where F(x, y) = (5x + 4y)i + 3xyj and C: r(t) = 3ri + rj, 0sts1 O…

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