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hello, i just wish to check that i have done the following correctly:

1. Evaluate [tex] \int d\overarrow{r} [/tex] (r is a vector, and its a closed integral) around the circle C represented by [tex]x^2 + y^2 = a^2[/tex]

what i did here was switch to polars and called [tex]d\overarrow{r}[/tex] ->[tex]rd\theta[/tex] then i noted that r=a and integrated from 0 to 2pi to get the answer as 2pi * a.

and

2. If [tex]\overarrow{f} = x\hat{x} + y\hat{y} + z\hat{z}[/tex]

evaluate [tex]\int \overarrow{f} \cdot d\overarrow{r} [/tex] from (0,0,0) to (1,1,1) along

a) a straight line connecting these points

b) a path from (0,0,0) to (1,0,0) to (1,1,0) to (1,1,1)

for both of these i ended up getting 3/2

for a i just replaced y and z by x and dy and dz by dx and integrated 3x dx...

and for b i got 3/2 by adding up three integrals so i think this should be correct? thanks

1. Evaluate [tex] \int d\overarrow{r} [/tex] (r is a vector, and its a closed integral) around the circle C represented by [tex]x^2 + y^2 = a^2[/tex]

what i did here was switch to polars and called [tex]d\overarrow{r}[/tex] ->[tex]rd\theta[/tex] then i noted that r=a and integrated from 0 to 2pi to get the answer as 2pi * a.

and

2. If [tex]\overarrow{f} = x\hat{x} + y\hat{y} + z\hat{z}[/tex]

evaluate [tex]\int \overarrow{f} \cdot d\overarrow{r} [/tex] from (0,0,0) to (1,1,1) along

a) a straight line connecting these points

b) a path from (0,0,0) to (1,0,0) to (1,1,0) to (1,1,1)

for both of these i ended up getting 3/2

for a i just replaced y and z by x and dy and dz by dx and integrated 3x dx...

and for b i got 3/2 by adding up three integrals so i think this should be correct? thanks

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