But we multiplied it by an integrating factor.

It doesn't matter which one we pick, which integrating factor this is called the integrating factor which integrating factor we pick.

So we'll learn about integrating factors.

So we have our integrating factor.

Anyway, we now have our integrating factor.

So we're integrating with respect to y first.

Because I was interested in integrating these two worlds,

You now know a little bit about integrating factors.

Well, the first integral I'm integrating with respect to x.

Now, integrating chemistry in computation, where the bits are bubbles.

We're just trying to figure out the integrating factor right here.

Architects should collaborate with other professionals more to make this messy environment more beautiful by integrating fragmentary elements in urban space.

And then that has to equal our new N, or the new expression we got after multiplying by the integrating factor.

And in the previous video, we figured out that a possible integrating factor is that we could just multiply both sides by x.

Here's something where we're sort of integrating a bunch of different capabilities here.

So in the next video, we're now going to use this integrating factor.

Let me finish by saying that my personal design issue for the future is really about integrating, to think about that intuitive and that analytical.

Engineering can be inspired by biology by using its principles and analogies when they're advantageous, but then integrating that with the best human engineering, ultimately to make something actually better than nature.

System integrators, not only supporting, servicing, and integrating your products but potentially tens of others.

And we're integrating this now with a whole era of cellular engineering, and integrating exponential technologies for essentially 3D organ printing replacing the ink with cells and essentially building and reconstructing a 3D organ.

So, where do you start when you have a program that's about integrating lives with passions?

Using just your first year calculus derivative and integrating skills, you can solve a separable equation.

But this whole effort is generated, is driven, by IT as well because that is how we're gathering all this information, and linking it, and integrating it together.

We're also, on top of that, integrating wireless networking into an affordable device with GPS and GSM.

Or you could kind of view it I'm holding y constant and integrating along the x axis.

And those can all be made more efficient, and the motors that turn them can have their system efficiency roughly doubled by integrating 35 improvements, paying back in about a year.

And if your brain is failing at integrating bad news about the future, you will constantly leave your rose tinted spectacles on.

And the other is Moksha Yug Access, which is integrating rural supply chain on the foundations of self help group based microfinance.

So you really see how this kind of crowd sourced imagery is integrating, in a very deep way, into the map itself.

Well, it's going to be the density function, x squared yz times the volume differential, but we're integrating with respect to z first.

But the thing that was true, the expo was about the future of cities, and particularly the Victorians pioneered integrating nature into the cities.

We also want to look at ways of matchmaking and putting funding partners together, and the idea of integrating manufacturers fab labs in every country.

And then you realize that by integrating aspects of tradition and community into their struggles, women like Sakena and Leah and Leymah but also women like Sonia Gandhi here in India and Michelle Bachelet in Chile and Shirin Ebadi in Iran are doing something else.

All of these are in the lab pushing further and further and further, not as metaphor but literally integrating bits and atoms, and they lead to the following recognition.

Also in London, and in Europe across the board, they're very advanced in their use of green rooftops and integrating beehives, and I'll show you an ending note here.

By guile and by bluster, by night and by day,

So, it was a rough it was a rough go, but I fell in love with this process of actually integrating graphics into architecture because I didn't know what I was doing.

The brain has this complex task of putting together, integrating, subsets of these regions into something that's more meaningful, into what we would consider to be objects, as you see on the right.

Stand by. Stand by.

They are intimidated by warlords, by terrorists, by criminals.

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One, by one, by one.

By birth and by choice,

Workers, by hand, by brain.

Not by preaching, not by telling, not by reading, but by addressing your mind.