Through the vent.

Integral

Can you vent the antimatter?

Gotten into the vent yet?

Integral step

Show integral

Integral step

He gave vent to his disappointment.

Sometimes they just need to vent.

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.

Not a single vent opening or anything.

That vent is guarded by a laser net.

We're showing a breach on an exterior vent.

It usually designates some kind of heating vent.

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.

He is apt to give vent to his feelings.

He is apt to give vent to his feelings.

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?

We gotta vent the compartment! Venting complete. Fires are out.

Air

Air.

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.

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

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.