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.

















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)
_____________________________________________________________

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.