Calculus 3 Quiz
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VECTOR FIELDS & LINE/SURFACE INTEGRALS
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Let f(x,y,z)=x2yz+xy2z+xyz2f(x,y,z) = x^2yz + xy^2z + xyz^2. The gradient field F=∇f\mathbf{F} = \nabla f is used to compute ∫CF⋅dr\int_C \mathbf{F} \cdot d\mathbf{r} where CC is the intersection of the sphere x2+y2+z2=9x^2 + y^2 + z^2 = 9 with the plane x+y+z=3x + y + z = 3, oriented counterclockwise when viewed from the origin. What is the value of this line integral?
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