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# 2 C4 integration questions im stuck on watch

1. Hi all,
Can anyone help me out with these two questions, I spent some time on them then gave up and moved on but now their really starting to bug me so I would appreciate some help. Thanks

Use substitution u=lnx to show that Integral(e^2x to e) 1/x(sqrt)lnx dx. is equal to 2 root 2 -1

Sorry hope u can understand what ive written, im trying to learn to use latex
2. (Original post by Virgil)
Hi all,
Can anyone help me out with these two questions, I spent some time on them then gave up and moved on but now their really starting to bug me so I would appreciate some help. Thanks

Use substitution u=lnx to show that Integral(e^2x to e) 1/x(sqrt)lnx dx. is equal to 2 root 2 -1

Sorry hope u can understand what ive written, im trying to learn to use latex
Sorry, I can't follow that. If your Latex isn't up to it, try specifying the limits and what you're integrating separately, and liberal use of brackets to make things clear.
3. Okay well the limits of the integral are e^2x to e
The bit after the integral is (1) divided by the ((square root of (lnx) times) times x) dx.

And the answer is suppose to be (2root2)-2

Hope thats abit clearer thank you
4. I'm somewhat puzzled by your lower limit: e^2x is a function of x, or am I being particularly thick at the moment.
5. that what is says on the question Integral from e^2x at the top to e at the bottom
6. idiots
7. OK, this is what I think the question should be:

Does that seem reasonable from what you've got?

If so, how far have you got?
8. So first ive found that u=lnx so du/dx=1/x therefore dx=x.du so now I replace the dx with x.du

So my equation so far is the integral of limits 1/x(sqrt u) times by x.du

So the x cancels on top and bottom to leave 1/(sqrt U) du. Rights so far?

This is the bit im stuck on how do I change the limits so that they are in terms of du and not dx?
9. and the answer should have the (-1) outside the bracket of the 2root2 bit
The equation bit is right
10. sorry mu fault i miss read the question YOU are RIGHT it cant be e^2x it is e^2 SORRY
11. (Original post by Virgil)
So the x cancels on top and bottom to leave 1/(sqrt U) du. Rights so far?
That's the correct integral.

This is the bit im stuck on how do I change the limits so that they are in terms of du and not dx?
I'll rephrase that "in terms of u and not x".

Just use the substitution "u= ln x". E.g. for the upper limit you'll have , which is...?
12. ah right so now the upper limit is just 2 and the lower limit is now 1
13. (Original post by ghostwalker)
That's the correct integral.

I'll rephrase that "in terms of u and not x".

Just use the substitution "u= ln x". E.g. for the upper limit you'll have , which is...?
Im a little confused as to how to go about the next step, the integral of 1/(root)u .
14. U dont use the ln rule and ive tried just integrating normally and I dont get 2root2 -1
15. (Original post by Virgil)
Im a little confused as to how to go about the next step, the integral of 1/(root)u .
You'll kick yourself!

Rewritiing it as

Can you see?
16. (Original post by Virgil)
U dont use the ln rule
I don't understand what you are talking about there.

Also I never said you got to 2root2 -1. I got to 2(root2-1), as per my previous posting.

Edit: I've just run it through some graphing software, and if that integral is correct, then the answer is 2(root2-1), and not 2root2-1
17. FML the answer in the book says it is 2root2 -2 not -1. FML
18. (Original post by Virgil)
U dont use the ln rule and ive tried just integrating normally and I dont get 2root2 -1
I follow you now. Yes, you want to integrate normally, (ln rule not required). The answer is 2root2 -2 or 2(root2-1)
19. (Original post by ghostwalker)
I don't understand what you are talking about there.

Also I never said you got to 2root2 -1. I got to 2(root2-1), as per my previous posting.

Edit: I've just run it through some graphing software, and if that integral is correct, then the answer is 2(root2-1), and not 2root2-1
The ln rule is where f(x) divided by f'(x) = ln(f(x)) +c

Sorry buddy
20. Cool.

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