00:01
Well, this problem we want to find the value of the integral from the u infinity to 0 of x times 2 to the x.
00:07
Now, i use integration by parts here, and so let's let u be x.
00:13
Let's let dv be 2 to the x d x, this means d u is d x, and v is 2 to the x over the natural out of 2.
00:27
And so this integral becomes u times v, so x times 2 to the x over the natural out of 2, minus the integral of v to you.
00:45
So now if we integrate again, the antide derivative of 2 to the x is 2 of the x over the natural order of 2.
00:51
So now we'll have 2 natural order of 2 is on the bottom.
00:55
And then we still have this first one here.
01:01
This is from negative infinity to 0.
01:05
And so this is the limit as x goes to negative infinity with x times 2 to the x over the natural order of 2, minus 2 to the x over the natural large square out of 2.
01:19
Actually, that comes second...