## February 05, 2007

### Scribe Post

Hey everyone! I tried making my scribe as a stop-action animation but I couldn't get it to work right so I guess I'll make it the old way...

With this definite integral, we can find its antiderivative and find the area.

Let's take a look at the graph...

Solving problems like this are not always this easy as this one. We can't always find the exact value of the definite integral.

Take a look at this problem and its graph.

We could use Riemann sums to find the area under the curve.

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These are the differentiation and integration formulas. We use these to help us determine the problems below.

Determine:

1)
Use substitution. (I FORGOT TO PUT dx INTO THE PICTURE)
u= x 3
du= 3x2
1/3du= x2 dx

If your wondering why u = x3 its because

(x3)2 = x6. So u is u2. We are trying to make the original function look like d/dx Arctan(x) integration formula.

Substitute ....................................................Resubstitute

You don't need " + C " in the intermediate steps because the C are not the same while your substituting.

(There's supposed to be an equal (=) sign in between the pictures)
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2)
If the 8 was a 9 in the polynomial we could complete the square.
So we do this,
6x-x2 -8 Factor out the negative.
-[(x2 -6x+8 +1) -1]
-[(x2 -6x+9) -1]
-[(x-3)2 -1]
1 - (x-3)2 We can replace this into the integral.

Next we use substitution.

Let u = x+3

du = dx

Then RE-substitute..

And we're done

Homework: finish up arctrig exercises (7.5)

Wednesday's scribe will be Katrin.

e said...

Hi Ashlynn,

I have a question about #1 if you don't mind. You said:

u= x 3
du= 3x2
1/3du= x2 dx

but your integral has only xdx. Is it a typo or am I not seeing something obvious? Thanks,

e

ashlynn said...

Yes that is a typo. Thank you for telling me.

The picture was supposed to read X squared.