# 2 vector integration problems

• Feb 28th 2013, 06:28 AM
DonnieDarko
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)

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:)
• Feb 28th 2013, 03:51 PM
chiro
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)?
• Feb 28th 2013, 10:14 PM
DonnieDarko
Re: 2 vector integration problems
Actually I solved first one, so I'll try some more for second, and share toughts ;)