My scribe for the class blog apcalc07.blogspot.com

1. Alright so today was
all about a technique
used to solve
antiderivatives

3. We started with antidifferentiating this:

4. First identify the inner function

5. Let this inner function, referenced in
more complicated cases as quot;beastquot;, equal
to some variable commonly quot;uquot;

6. We find the derivative of quot;uquot;

7. Set this derivative equal
to the stuff outside the
parent function

8. Substitute in quot;uquot; and du in
appropriate places and bring
coefficients out of the
antiderivative

9. In this step we
antidifferentiate the
square root of u times du.
By chain rule when you
differentiate sqr(u) you
will get du so du is
already dealt with because
we are using u. We run
our differentiation rule
backwards for sqr(u) to
get our other constant
multiplier and u^(2/3).

10. Substitute our value for
u in relation to x back
in to get our answer for
the antiderivative.

11. Now with a little more efficiency...

12. Now with a little more efficiency...
Inner function

13. Now with a little more efficiency...
Inner function
Chained function

14. Now with a little more efficiency...
Inner function
Chained function
Substituting in and moving
constant

15. Now with a little more efficiency...
Inner function
Chained function
Simple antidifferentiation

16. Now with a little more efficiency...
Inner function
Chained function
Re­substitute and
simplify

17. Now with a little more efficiency...

18. We then did an easier one that
I'm not going to bother with
because there is nothing new, if
you wish to see it then Mr.K's
slides are right below this post.

19. Now one that doesn't work out as
nicely

21. Easier to visualize
sometimes if you break
it apart

22. Stating u and du, your
choice here, you can
use sqr(x +7) or just
x + 7 as your inner
function

23. Substitute in... but
we are still left with
an x and we can't
antidifferentiate with
two variables...

24. Solve for x

25. Substitute in
for x

26. Simplify and
antidifferentiate

27. Substitute back in the x's
and simplify

28. If it is a definite integral then evaluate your
answer on that interval or evaluate your other
function with u on the interval found by running
the two endpoints through your function for u.