My mind is escaping me

**penguinpwn** · January 31st 2010, 04:56 PM

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:
$<br /> \int_0^1 \frac{1}{2^x}dx$

**zhupolongjoe** · January 31st 2010, 05:02 PM

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).

**TWiX** · January 31st 2010, 05:07 PM

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:
$<br /> \int_0^1 \frac{1}{2^x}dx$

$\frac{1}{2^x}=(\frac{1}{2})^x$ .

**Plato** · January 31st 2010, 05:58 PM

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

**Bruno J.** · January 31st 2010, 06:12 PM

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?

**HallsofIvy** · February 1st 2010, 04:06 AM

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.

**mr fantastic** · February 2nd 2010, 02:12 AM

This thread can be continued in the Philosophy subforum (if so desired).

Thread closed.

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