(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate Int{(y+yz cos(xyz))dx + (x^2+xzcos(xyz)dy + (z + xycos(xyz)dz}

along the ellipse:

x = 2cost

y = 3sint

z = 1

2pi=>t>=0

(its a line integral problem)

2. Relevant equations

3. The attempt at a solution

I have tried the following things:

First, i tried plugging x,y,and z into the integral, finding dx, dy, and dz in terms of the parameter t. However, doing so i get an expression that cannot be solved using elementary functions:

Int{(3sint+3sint cos(2cost*3sint))dx + ((2cost)^2+2cost*cos(2cost*3sintz)dy + (1 + 2cost*3sint*cos(2cost*3sint)dz}

dx = -2sint dt

dy = 3cost dt

dz = 0

gives me the following:

Int{(3sint+3sint cos(2cost*3sint))(-2sint dt) + ((2cost)^2+2cost*cos(2cost*3sintz)(3cost dt)}

the above cannot be solved (according to my calculator) with elementary functions...

I also tried to simply eliminate t and to work from there using the following expression for the elipse:

x^2/4 + y^2/9 = 1

However, doing so I cannot get a solvable integral either because it leaves me with too few equations for the 3 unknowns ( i need to use the parameter t somehow, is what I am taking in from this). Is there anything else that I can try to solve this integral? absolutely any help would be greatly appreciated!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# This integral is destroying my life

**Physics Forums | Science Articles, Homework Help, Discussion**