Fundamental Theorem for Line Integrals · Calculus 3

Calculus 3 Quiz

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VECTOR FIELDS & LINE/SURFACE INTEGRALS

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Consider the vector field

\mathbf{F}(x,y) = (2xy + 3y^2)\mathbf{i} + (x^2 + 6xy - 1)\mathbf{j}

. If

C

is any smooth curve from point

(1,0)

to point

(2,3)

, what property must be verified before applying the Fundamental Theorem for Line Integrals, and what is the value of

\int_C \mathbf{F} \cdot d\mathbf{r}

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