M408C - Brian's Draft Cheat Sheet - Area BTW Curves -Find...

Area BTW Curves
-Find Intercepts
-Integrate Between Intercepts
+ Want Positive Area
Hyperbolic Trig
+ c
+ c
Critical Points
-CP =
First Derivative Test
- Separate interval according to intercepts
-
Find the sign of on each interval
-
-
Integration by Parts
Trig Substitution
Product of Trig Functions
- M odd
o
Save 1 and write the rest as sin x; U = sin x
- N Odd
o
Save 1 sin x and write the rest as cos x; U = cos x
- Otherwise: Everything as sin x; Use recursion formulas
- M Odd, N ≥ 1
o Save tan x sec x ; write rest as sec x ; u = sec x
- N Even, M ≥ 2
o
Save
- Otherwise: Everything in sec x; use recursion formula
- N Odd
o
Save sin x, write the rest as cos x: u = cos x
- Otherwise: Write everything in terms of cos x