# My mind is escaping me

• Jan 31st 2010, 04:56 PM
penguinpwn
My mind is escaping me
I seem to be having a huge case of mind lock, i can't seem to remember how to solve for the original function to evaluate the integral:
$\displaystyle \int_0^1 \frac{1}{2^x}dx$
• Jan 31st 2010, 05:02 PM
zhupolongjoe
Note that 1/(2^x)=2^-x.

Also recall that d/dx(2^x)=log(2)*2^x

So our integral is -1/log(2) * 2^(-x)+C. We now this because when we take the derivative, we have a -log(2) to get rid of so that we will be left with 2^(-x) (evaluate between 0 and 1 of course).
• Jan 31st 2010, 05:07 PM
TWiX
Quote:

Originally Posted by penguinpwn
I seem to be having a huge case of mind lock, i can't seem to remember how to solve for the original function to evaluate the integral:
$\displaystyle \int_0^1 \frac{1}{2^x}dx$

$\displaystyle \frac{1}{2^x}=(\frac{1}{2})^x$.
• Jan 31st 2010, 05:58 PM
Plato
BTW: It is impossible for "My mind is escaping me".
One's mind is simply one's brain.
• Jan 31st 2010, 06:12 PM
Bruno J.
Quote:

Originally Posted by Plato
BTW: It is impossible for "My mind is escaping me".
One's mind is simply one's brain.

Wouldn't that be like saying that my heartbeat is my heart?
• Feb 1st 2010, 04:06 AM
HallsofIvy
Quote:

Originally Posted by Plato
BTW: It is impossible for "My mind is escaping me".
One's mind is simply one's brain.

That is not true. "mind" and "brain" are NOT synonymous.
• Feb 2nd 2010, 02:12 AM
mr fantastic
This thread can be continued in the Philosophy subforum (if so desired).