(a) Find a function f such that F = ∇ f and (b) use part (a) to evaluate ∫C F · dr along the given curve C.
18. F(x, y, z) = sin y i + (x cos y + cos z) j − y sin z k,
C: r(t) = sin t i + t j + 2t k, 0 ⩽ t ⩽ π/2
To find: The potential function f such that .
Vector field is .
Write the relation between the potential function f and vector field .
Substitute for ,
Compare the equation with .
Integrate equation (1) with respect to x.
Apply partial differentiation with respect to y on both sides of equation (4).
Compare the equations (2) and (5)
The value of along the curve C.
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