Opener:
2x
d
x
=
∫ x2 − 2
∫
(e x si n(e x ))d x =
U-Substitution and the FTC
Let’s combine what we know about both of these ideas!
How does your process change
now?
5
2x
dx =
2
∫1 x − 2
10
∫3
(e x si n(e x ))d x =
A couple of things…
Remember that it is good practice for all the parts of
your integral to be in terms of the same variable. So,
You must either change your limits of integration to
being in terms of u,
Or, you must put in a “filler” for your limits of
integration to show that they are in terms of another
variable.
Decide on a process, and be consistent in that process.
More examples
1
∫−1
x2
x3 + 9
dx =
16
∫2 2x
1
ln x
dx =
More Examples
π
3
∫0
4si n x
dx =
1 − 4cos x
4
∫1
6
x
x
dx =
And Still More!!!
1
∫0
x +2
4 − 4x 2
dx =
ILO…
Section 5.9
Pg. 393-394 problems 5-49 odd
Section 5.10
Pg. 406-408 problems 13-37 odd