calculus II

1. Math 1230
Formula List
1. Euler’s Method

y n1  y n  hy n
2. Centroid
 
b b
xf ( x) dx
1
 f ( x)2 dx
2
x y
a a
,
 
b b
f ( x) dx f ( x) dx
a a
3. Taylor Series
f (c) f ( n ) (c )
f ( x)  f (c)  f (c)( x  c)  ( x  c) 2    ( x  c) n  
2! n!
for n  0, 1, 2, 3, 
4. Differentiating and Integrating of Power Series

If f ( x)   a ( x  c)
n 0
n
n

 na ( x  c)
d n 1
Then (a) f (x)  n
dx n 1

  n  1 ( x  c)
x
an n 1
(b) f ( x) dx 
0
n 0