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I have to find the work done by

$$f(x,y,z)= \left( x \cos(xz)e^y, \, z \cos(xz) e^y, \, \sin(xz) e^{y+1} \right)$$

which is parameterized by $L(t)=(2-t,3,t^3)$ where $t$ is from 0 to 1. I know that the formula for work is then line integral by

$$\int F(r(t)) \cdot r'(t) \, dt.$$

I'm pretty sure this is how to do the problem, but it's mathematically really tedious so I feel like I'm missing something. Can anyone confirm this is the correct approach to the problem or am I missing an alternative method?

Mark Fantini
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Tony
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1 Answers1

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This is the way to go. Realize that $y$ is constant, therefore the $dy$ component will vanish and you will have (a bit) less trouble.

Mark Fantini
  • 5,523