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Let vec{F} = (6z + 6x^2) vec{i} + (4y + 6z + 6 sin(y^2)) vec{j} + (6x + 6y + 4e^{z^2}) vec{k}. (a) Find curl vec{F}. curl vec{F} = (b) What does your answer to part (a) tell you about int_C vec{F} cdot dvec{r} where C is the circle (x - 35)^2 + (y - 10)^2 = 1 in the xy-plane, oriented clockwise? int_C vec{F} cdot dvec{r} = (c) If C is any closed curve, what can you say about int_C vec{F} cdot dvec{r}? int_C vec{F} cdot dvec{r} = (d) Now let C be the half circle (x - 35)^2 + (y - 10)^2 = 1 in the xy-plane with y > 10, traversed from (36, 10) to (34, 10). Find int_C vec{F} cdot dvec{r} by using your result from (c) and considering C plus the line segment connecting the endpoints of C. int_C vec{F} cdot dvec{r} =

          Let vec{F} = (6z + 6x^2) vec{i} + (4y + 6z + 6 sin(y^2)) vec{j} + (6x + 6y + 4e^{z^2}) vec{k}.
(a) Find curl vec{F}.
curl vec{F} =
(b) What does your answer to part (a) tell you about int_C vec{F} cdot dvec{r} where C is the circle (x - 35)^2 + (y - 10)^2 = 1 in the xy-plane, oriented clockwise?
int_C vec{F} cdot dvec{r} =
(c) If C is any closed curve, what can you say about int_C vec{F} cdot dvec{r}?
int_C vec{F} cdot dvec{r} =
(d) Now let C be the half circle (x - 35)^2 + (y - 10)^2 = 1 in the xy-plane with y > 10, traversed from (36, 10) to (34, 10). Find int_C vec{F} cdot dvec{r} by using your result from (c) and considering C plus the line segment connecting the endpoints of C.
int_C vec{F} cdot dvec{r} =

Let vecF = (6z + 6x^2) veci + (4y + 6z + 6 sin(y^2)) vecj + (6x + 6y + 4e^z^2) veck.
(a) Find curl vecF.
curl vecF =
(b) What does your answer to part (a) tell you about intC vecF cdot dvecr where C is the circle (x - 35)^2 + (y - 10)^2 = 1 in the xy-plane, oriented clockwise?
intC vecF cdot dvecr =
(c) If C is any closed curve, what can you say about intC vecF cdot dvecr?
intC vecF cdot dvecr =
(d) Now let C be the half circle (x - 35)^2 + (y - 10)^2 = 1 in the xy-plane with y > 10, traversed from (36, 10) to (34, 10). Find intC vecF cdot dvecr by using your result from (c) and considering C plus the line segment connecting the endpoints of C.
intC vecF cdot dvecr =

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