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Integration of exponential

Integration of exponential:

I am having difficulty integrating exponential. I want to compute the indefinite integral of r`(t)
where r`(t) is the vector <3, -e(^ -t), 0>

The first integration I have is <3t+c1, ------- c3>

I am not sure how to integrate the -e^-t

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I also have a similar question in a triple integral problem

We have:

I from 1 to 4 ... I from 0 to 1.... and I from 0 to X (going from left to right)
and the function we want to integrate is 2Ze^-x^2 dy dx dz

I am having trouble working out the mechanics of this integral mainly because of the e^-x^2
(e to the minus x^2)

Any assistance is appreciated.

Solution Summary

This solution is comprised of a detailed explanation to compute the indefinite integral of r`(t)
where r`(t) is the vector <3, -e(^ -t), 0>.

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