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Stupid silly question on integration.

I've had a mind block and completely forgotten how to integrate 12/t lol. I can't believe I've forgotten but indeed I have.

Logzzzz.

If it's the integral of f'(x) / f(x), the answer is ALWAYS log(f(x)) !
What that means is that if the bottom line differentiates into the top line, the answer is ALWAYS log(bottom line) :smile:

.

you're going to have to be sneaky and take a factor of 12 outside the bracket here though - but hopefully this has jogged your memory!

Reply 3

0le

OP

21

majikthise

Logzzzz.

It's a parametric equation where the question asked me to find the volume of it in terms of 2 pie or something like that. The integral has been simplified to 12/t :s

∫ 12t-¹ dt

Just seen the post above. Yes, I understand taking the 12 outside. I don't remember the logs stuff tho :frown:

its 12ln|t| + C

OP

AsimSr2704

its 12ln|t| + C, or ln|12t| +C?

Oh Yeah

Thanks lol!!! I can't believe I forgot that. I remember now. if its a constant over (something) then the integral is always ln something. If that something has a power though, then its the normal rules. Thanks :wink:

Reply 6

M_E_X

14

djpailo

It's a parametric equation where the question asked me to find the volume of it in terms of 2 pie or something like that. The integral has been simplified to 12/t :s

∫ 12t-¹ dt

Just seen the post above. Yes, I understand taking the 12 outside. I don't remember the logs stuff tho :frown:

the answer is

I = 12log(t) + C

(log base 10).

Read my post again, about if the top line differentiates to the bottom line...
You might understand this time. This is a really important technique which comes up time and time again, and often you're expected to spot it without it being hinted at. (at A-level standard).

Reply 7

AsimSr2704

Oh Yeah Thanks lol!!! I can't believe I forgot that. I remember now. if its a constant over (something) then the integral is always ln something. If that something has a power though, then its the normal rules. Thanks

you're welcome, but the second answer i gave was wrong :biggrin:

, it's 12ln|t| +C, becuase, to integrate k/x, you have to make it kln|x| + C, sorry for that mistake!

Reply 8

AsimSr2704

It's a parametric equation where the question asked me to find the volume of it in terms of 2 pie or something like that. The integral has been simplified to 12/t :s

∫ 12t-¹ dt

Just seen the post above. Yes, I understand taking the 12 outside. I don't remember the logs stuff tho

To find volume of revolution, you need to integrate the square of the function, and multiply it by pi.

Reply 9

Bezzler

1

M_E_X

the answer is

I = 12log(t) + C

(log base 10).

Read my post again, about if the top line differentiates to the bottom line...
You might understand this time. This is a really important technique which comes up time and time again, and often you're expected to spot it without it being hinted at. (at A-level standard).

Log base e! Otherwise known as ln. Definitely not log base 10! It's because when you differentiate/integrate e^x you get e^x (+ c if integrating), I think, or something to do with that.

Reply 10

Hellier

8

exp(x) = sum(x^n/n!) from n=0 to n = infinity
as you can see, this is the only function which differentiates to give itself.

Reply 11

Gaz031

15

Provided the original poster can prove the series has infinite radius of convergence and can prove the standard theorem about differentiation inside the radius of convergence...

Reply 12

M_E_X

14

Bezzler

Log base e! Otherwise known as ln. Definitely not log base 10! It's because when you differentiate/integrate e^x you get e^x (+ c if integrating), I think, or something to do with that.