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The value of the line integral ∫_P^Q (z² dx + 3y² dy + 2xz dz) along the straight line joining the points P (1,1,2) and Q (2,3,1) is

1. 20
2. 24
3. 29
4. -5

Correct answer: 24

Solution

The field (z^2,3y^2,2xz) is conservative with potential phi = x z^2 + y^3. The integral equals phi(Q)-phi(P) = (2*1+27) - (1*4+1) = 29 - 5 = 24, not -5.

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