calculus-triple integrals

nat190898 said:
Can someone please solve this and show the steps? Thanks in advance.View attachment 15092
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Were you instructed to use base 10 for \(\displaystyle \log(x)~?\)
I ask because the trend us usage is quite the other way.
Using \(\displaystyle \log(x)\) as the natural logarithm makes this question easier.
 
pka said:
Were you instructed to use base 10 for \(\displaystyle \log(x)~?\)
I ask because the trend us usage is quite the other way.
Using \(\displaystyle \log(x)\) as the natural logarithm makes this question easier.
Click to expand...
Yes. The question says to take log x as log to base 10 x as an assumption.
 
No, sorry, but no one here will show you how to do this step by step. We will however help you do it step by step. Can you show us your attempt at this problem or tell us where you are stuck?

Can you do the inner most integral, the one with respect to dx? Just treat y and z as constant. Please post back with your work.
 
Jomo said:
No, sorry, but no one here will show you how to do this step by step. We will however help you do it step by step. Can you show us your attempt at this problem or tell us where you are stuck?

Can you do the inner most integral, the one with respect to dx? Just treat y and z as constant. Please post back with your work.
Click to expand...
This is what I did but when replacing the limits after having integrated wrt x, I end up with a logarithmic function that i do not know how to integrate
 

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Jomo said:
No, sorry, but no one here will show you how to do this step by step. We will however help you do it step by step. Can you show us your attempt at this problem or tell us where you are stuck?

Can you do the inner most integral, the one with respect to dx? Just treat y and z as constant. Please post back with your work.
Click to expand...
Also thank you very much for your response
 
Please check the limits on the second integral sign there is an x there and should no be.
On the log I hope you find some one other that me to help.
For me there are only natural logarithms.
 
To clarify what you have been told:

The integral as given makes no sense; in order to take the limits of integration as shown, the differentials ought to be reordered, as dz dy dx, so that the inside integral is with respect to z. If the inner integral is with respect to x, then is "uses up" the x, and there can be no x in any of the limits.

As for carrying out the integral, I would start by rewriting the integrand as [MATH]e^x e^y e^z[/MATH], which will make some steps easier.

Also, since calculus works best with natural logs, as soon as it matters you will want to rewrite log(x) as ln(x)/ln(10).

So please confirm what the problem you were given says, and then try again. We'll be glad to help you refine your work, once you are doing a sensible problem.
 
Check your assumptions list. [math]e^{log(f(x))} \neq log(f(x))[/math], even if we are using [math]log_e \equiv ln[/math]. To demonstrate just let f(x) = 1.

-Dan
 
topsquark said:
Check your assumptions list. [math]e^{log(f(x))} \neq log(f(x))[/math], even if we are using [math]log_e \equiv ln[/math]. To demonstrate just let f(x) = 1.

-Dan
Click to expand...
I think it was "hand-writing-po" - should have stated:

[math]e^{log(f(x))} \ = \ \ f(x)[/math]
 
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