Hi everyone.(adsbygoogle = window.adsbygoogle || []).push({});

I am going through examples for maths exams and am unsure on the final part of a question I am attempting so hoping you may help me?

1. The problem statement, all variables and given/known data

"Let C be the closed, piecewise smooth curve comprising individual curves C1 and C2

defined by r1 = (x, x2, 1) and r2 = (x,+√x, 1), respectively, with 0 ≤ x ≤ 1, see

Figure 1. Evaluate the work done by the vector field ∇ on a particle moving around

curve C once in the anticockwise direction, i.e. directly compute the integral

[tex]\oint \nabla \theta (x,y,z) dr[/tex]"

2. Relevant equations

As per above/below

3. The attempt at a solution

[tex]\theta (x,y,z) = x^2z^2+3yz+2x[/tex]

hence

[tex]\nabla \theta (x,y,z) = (2xz^2+2, 3z, 2zx^2+3y)[/tex]

So, using green's theorem (I think this is correct)

[tex]\oint \nabla \theta (x,y,z) dr[/tex]

is the same as

[tex]\int_{y=x^2}^{y=\sqrt{x}}\int_0^1 \nabla \theta (x,y,z) dxdy[/tex]

I think this is correct, but cant seem to find the next "step". Id be grateful if anyone could tell me if Im on the right track, and maybe show me where to go on the next step?

Thanks in advance

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# Homework Help: Line Integral Problem

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