Integral

He gave vent to his disappointment.

Integral step

Show integral

Integral step

Anyway, I'm not going to vent on.

This is what's called a hydrothermal vent.

Who gets to go into the vent?

Let him give vent to his fury

Come here! There's an airconditioning vent here.

That vent is guarded by a laser net.

He is apt to give vent to his feelings.

He is apt to give vent to his feelings.

And when you do the integration by parts, this could be an indefinite integral, an improper integral, a definite integral, whatever.

And that's taking the integral.

And this vent fluid is about 600 or 700 degrees F.

Set here the spatial integral step.

Anyway, integral from 0 to infinity.

Minus this integral evaluated at 0.

That's what that double integral represents.

And what's the integral of this?

Air

And there's a whole new hydrothermal vent community that has been formed.

Let's now do another triple integral, and in this one I won't actually evaluate the triple integral.

So anyway, let's take the anti derivative and evaluate this improper definite integral, or this improper integral.

The integral of u prime times v.

And this is a definite integral, right?

And that's where the integral comes in.

So what's the integral of this thing?

Let's try to set up this integral.

That's the intuition behind the definite integral.

Let's just worry about the indefinite integral.

So how do we evaluate this integral?

I'll just use that old integral sign.

What happens if I take the integral?

Let me write a nicer integral sign.

Because the t's are involved in evaluating the boundaries, since we're doing our definite integral or improper integral.

And I appreciate being able to vent some of my anguish upon you.

Air speed

Oxygen Air

Air Pressure

Air pressure

The air conditioner isn't taking in enough air.

So we can rewrite this integral as y.

So what's this integral going to look like?