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EngageEngage

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## Homework Statement

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)

## Homework Equations

## 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!