Let F(x, y, z) = (3x2 yz – 3y) i + (x3z – 3x) j + (x3y + 2z) k
Evaluate ∫C F • dr, where C is the curve with initial point (0, 0, 2) and terminal point (0, 3, 0) shown in the figure.
To evaluate: The value of , where C is the curve with initial point and terminal point .
Consider the standard equation of an curl F for
Find the value of .
Substitute for , for and for in equation (2),
Since , the F is a conservative vector and the domain of F is .
Write the relation between the potential function f and vector field .
Substitute for ,
Compare the equation (3) and equation (1).
Integrate equation (4) with respect to x.
Apply partial differentiation with respect to y on both sides of equation (7).
Consider the value of
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