Test 1 Flashcards
(48 cards)
1
Q
Integration by Parts Formula
A
∫ udv = [uv - ∫( vdu )]
2
Q
d/dx C=
A
0
3
Q
d/dx x=
A
1
4
Q
d/dx (x^n)
A
n*x^(n-1)
5
Q
d/dx (Cx)=
A
C d/dx (x)
6
Q
d/dx (x*v)=
A
x * d/dx[v] + v* d/dx[x]
7
Q
d/dx (x/v)=
A
(( v * d/dx[x] - x * d/dx[v] )) / 2
8
Q
d/dx [(f*g)(x)]=
chain rule
A
f’(g(x)) * g’(x)
9
Q
d/dx e^x=
A
e^x
10
Q
d/dx (1/x)
A
-1/x^2
11
Q
d/dx a^x=
A
a^x * ln(a)
12
Q
d/dx ln |x|=
A
1/x
13
Q
d/dx loga |x|=
A
1 / (ln(a))x
14
Q
Lim as x-> ∞ of (f(x)/g(x))=
LH’opital’s Rule
A
f’(x)/ g’(x)
15
Q
∫x^n dx=
A
( x^(n+1) ) / (n+1)
16
Q
∫ 1/x^2 dx =
A
-1/x + C
17
Q
∫1/x dx=
A
ln (x) + c
18
Q
∫ 1/(x+3) =
A
ln (|x+3|) + C
19
Q
1
A
1
20
Q
d/dx [sinx] =
A
cos x
21
Q
∫ cos x dx=
A
sin x + C
22
Q
d/dx [cos x]=
A
- sin x
23
Q
∫-sin x dx=
A
cos x + C
24
Q
∫ sin x dx =
A
-cos x + C
25
d/dx [tan x] =
sec^2 x
26
∫ sec^2 x=
tan x + C
27
d/dx [cot x] =
-csc^2 x
28
∫ csc^2 (x) dx =
-cot x + C
29
∫ -csc^2 (x) dx=
cot x + C
30
d/dx sec x=
sec x tan x
31
∫ sec x tan x dx=
sec x + C
32
d/dx [csc x] =
-csc x cot x
33
∫ [-csc x cot x ] dx =
csc x
34
∫ [csc x cot x] dx =
-csc x
35
∫ [a^x] dx =
(a^x) /ln a
36
∫ sec^3 (x) dx =
1/2 (sec x tan x + ln(|sec x + tan x|) + C
37
∫ tan x dx=
ln (| sec x |) + C
38
∫ cot x dx =
ln (| sin x |) + C
39
∫ tan x dx =
ln (| sec x |) + C
40
∫ cot x dx =
ln (| sin x |) + C
41
∫ sec x dx =
ln (| sec x + tan x |) + C
42
∫ csc x dx =
- ln (| css x + cot x |) + C = (( ln (| csc x - cot x |) + C ))
43
∫csc^3 (x) dx =
- 1/2 (csc x cot x + ln (|csc x + cot x|) + C
44
45
46
47
cos^2 (x )=
1/2 (1+cos (2x))
48
sin^2 (x) =
1/2 (1 - cos(2x))
