# Evaluate an integral in 3D space

Is the integration process following P in Cartesian coordinates:

$$z = \cos(x^2+1), \qquad y=1$$

Evaluate

$$\int_{(0,1,\cos(1))}^{(1,1,\cos(2))}\hat{F}dl$$

Over the integration process P and where

$$\hat{F} = \tan(x)\hat{a}_{y}$$

I believe it's something that look like this.... but my cartesian coordinate given are different... I'm not sure about the parametric of my Cartesian coordinate.

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Is the question clear? –  fneron Jul 12 '12 at 20:22

## 1 Answer

1. Parametrize P. In other words, express x, y, z in terms of one variable, the parameter. Hint: one of x,y,z will work as parameter.
2. Differentiate x,y,z with respect to parameter.
3. Plug the parametrization from 1 into F.
4. Take dot product of the results of 2 and 3.
5. Integrate the result of 4 with respect to the parameter.

Had you explained where your difficulty lies, you might have received a more concrete advice.

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I'm sorry I didn't mention my actual difficulty... It's number 1, I know I have to parametrize my function, but I don't really know if I do it correctly. I believe, I have to put under a common variable each coordinates. Something, like x=t, y=1, z= cos(t2+1)... Is that correct? –  fneron Jul 13 '12 at 3:36
@fneron Yes that is correct. –  user31373 Jul 13 '12 at 3:46
thank you very much! –  fneron Jul 13 '12 at 3:49