00:01
So for this integral, before we actually compute it, since we have two terms here that are the same term when one's being raised two power, another one's being raised two power, this one's being raised the first, the one half, and they're being multiplied together, we can add the powers together of those two terms and say it's just w to the three halves power times dw, and now we can go ahead and find this integral.
00:25
And so the first thing we're going to want to do is take the constant out of the integral, so we have 10 times the integral.
00:30
Of w to the three halves power times dw.
00:34
And the next thing we want to do is use the power rule for anti -differentiation.
00:39
So i'm going to go ahead and write it over here, and it's just derived from the power rule for derivatives.
00:45
And so what it says is the integral of x the n -1 power is equal to x -the -n divided by n.
00:54
And so here, if we let n equal, or sorry, if we let n -1 equal three -haves, then n is going to be three - halves plus one.
01:01
So this is going to be 10 times w to three halves plus one, which is five halves...