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.


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


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)

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,


ashlynn said...

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

The picture was supposed to read X squared.