2 vector integration problems

1. Vector field is given with:

$\displaystyle \vec{F}=(3x^2yz+y^3z+xe^{-x})\hat{i}+(3xy^2+x^3z+ye^x)\hat{j}+(x^3y_y^3x_xy^ 2z^2)\hat{k}$

fin $\displaystyle \oint\vec{F}\cdot\mathrm{d}\vec{r} $ on a closed contour OABCDEO given with (0,0,0), (1,0,0), (1,0,1), (1,1,1), (1,1,0), (0,1,0), (0,0,0)

by linear roads.

2. Vector field is given with:

$\displaystyle \vec{F}=F_0\bigg[\bigg(\frac{y^3}{3a^3}+\frac{y}{a}e^{\frac{xy}{a^2 }}+1\bigg)\hat{i}+\bigg(\frac{xy^2}{z^3}+\frac{x+y }{a}e^{xy}{a^2}\bigg)\hat{j}+\frac{z}{a}e^{\frac{x y}{a^2}}\hat{k}\bigg] $

Using Stokes theorem find:

$\displaystyle \oint \vec{F} \cdot \mathrm{d}\vec{r} $

by curve which is perimeter of square ABCD given with A=(0,a,0), B=(a,a,0), C=(a, 3a, 0), D=(0,3a,0).

help pls:)

Re: 2 vector integration problems

Hey DonnieDarko.

Can you show us what you have tried? (Hint: For the first one think about the parameterization in terms of line segments).

In other words, what is the parameterization of each segment (and then take the inner product for that segment)?

Re: 2 vector integration problems

Actually I solved first one, so I'll try some more for second, and share toughts ;)