Integrals

studied byStudied by 8 people
4.0(1)
Get a hint
Hint

∫dx

1 / 97

flashcard set

Earn XP

Description and Tags

98 Terms

1

∫dx

knowt flashcard image
New cards
2

∫uⁿ du

knowt flashcard image
New cards
3

∫e^u du

knowt flashcard image
New cards
4

∫b^u*ln(b) du

knowt flashcard image
New cards
5

∫b^u du

knowt flashcard image
New cards
6

∫cosu du

knowt flashcard image
New cards
7

∫-sinu du

knowt flashcard image
New cards
8

∫sinu du

knowt flashcard image
New cards
9

∫sec²u du

knowt flashcard image
New cards
10

∫-cscu*cotu du

knowt flashcard image
New cards
11

∫cscu*cotu du

knowt flashcard image
New cards
12

∫secu*tanu du

knowt flashcard image
New cards
13

∫-csc²u du

knowt flashcard image
New cards
14

∫csc²u du

knowt flashcard image
New cards
15

∫du/√(1-u²)

knowt flashcard image
New cards
16

∫-du/√(1-u²)

knowt flashcard image
New cards
17

∫du/(1+u²)

knowt flashcard image
New cards
18

∫-du/u√(1-u²)

knowt flashcard image
New cards
19

∫du/u√(1-u²)

knowt flashcard image
New cards
20

∫-du/(1+u²)

knowt flashcard image
New cards
21

∫du/u

knowt flashcard image
New cards
22

∫tan u du

-ln|cos u|+C

New cards
23

∫cot u du

ln|sin u|+C

New cards
24

∫sec u du

ln|sec u+tan u|+C

New cards
25

∫csc u du

-ln|csc u+ cot u|+C

New cards
26

f(x)g'(x) + g(x)f'(x)

derivative of the multiplaction of two functions

<p>derivative of the multiplaction of two functions</p>
New cards
27

d/dx [f(x)/g(x)] =

quotient rule

<p>quotient rule</p>
New cards
28

f'(g(x))g'(x)

chain rule

<p>chain rule</p>
New cards
29

d/dx [ln|x|] =

knowt flashcard image
New cards
30

d/dx [a^x] =

knowt flashcard image
New cards
31

d/dx [log_a X] =

knowt flashcard image
New cards
32

∫- sinx

knowt flashcard image
New cards
33

∫secxtanx

knowt flashcard image
New cards
34

∫- cscxcotx

knowt flashcard image
New cards
35

d/dx [tanx]

knowt flashcard image
New cards
36

d/dx [cotx]

knowt flashcard image
New cards
37

∫cosx

knowt flashcard image
New cards
38

quotient rule

knowt flashcard image
New cards
39

derivative of a power

knowt flashcard image
New cards
40

chain rule

knowt flashcard image
New cards
41

derivative of an exponential function

knowt flashcard image
New cards
42

derivative of a natural log

knowt flashcard image
New cards
43

d/dx [a^x]

knowt flashcard image
New cards
44

derivative of a log base a

knowt flashcard image
New cards
45

d/dx [sinx]

knowt flashcard image
New cards
46

d/dx [cscx]

knowt flashcard image
New cards
47

d/dx [cosx]

knowt flashcard image
New cards
48

d/dx [secx]

knowt flashcard image
New cards
49

d/dx [tanx]

knowt flashcard image
New cards
50

d/dx [cotx]

knowt flashcard image
New cards
51

d/dx [arcsinx]

knowt flashcard image
New cards
52

d/dx [arccscx]

knowt flashcard image
New cards
53

d/dx [arccosx]

knowt flashcard image
New cards
54

d/dx [arcsecx]

knowt flashcard image
New cards
55

d/dx [arctanx]

knowt flashcard image
New cards
56

d/dx [arccotx]

knowt flashcard image
New cards
57

product rule

knowt flashcard image
New cards
58

f is continuous at x=c if...

knowt flashcard image
New cards
59

Intermediate Value Theorem

If f is continuous on [a,b] and k is a number between f(a) and f(b), then there exists at least one number c such that f(c)=k

New cards
60

Global Definition of a Derivative

knowt flashcard image
New cards
61

Alternative Definition of a Derivative

f '(x) is the limit of the following difference quotient as x approaches c

<p>f &apos;(x) is the limit of the following difference quotient as x approaches c</p>
New cards
62

∫-sin(x)

knowt flashcard image
New cards
63

∫sec²(x)

knowt flashcard image
New cards
64

∫-csc²(x)

knowt flashcard image
New cards
65

∫sec(x)tan(x)

knowt flashcard image
New cards
66

Extreme Value Theorem

If f is continuous on [a,b] then f has an absolute maximum and an absolute minimum on [a,b]. The global extrema occur at critical points in the interval or at endpoints of the interval.

New cards
67

Rolle's Theorem

Let f be continuous on [a,b] and differentiable on (a,b) and if f(a)=f(b) then there is at least one number c on (a,b) such that f'(c)=0 (If the slope of the secant is 0, the derivative must = 0 somewhere in the interval).

New cards
68

Mean Value Theorem

The instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line.

<p>The instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line.</p>
New cards
69

First Derivative Test for local extrema

knowt flashcard image
New cards
70

Point of inflection at x=k

knowt flashcard image
New cards
71

Combo Test for local extrema

If f'(c) = 0 and f"(c)<0, there is a local max on f at x=c.
If f'(c) = 0 and f"(c)>0, there is a local min on f at x=c.
If f'(c) = 0 and f"(c)<0, there is a local max on f at x=c.
If f'(c) = 0 and f"(c)>0, there is a local min on f at x=c.
New cards
72

Horizontal Asymptote

knowt flashcard image
New cards
73

L'Hopital's Rule

knowt flashcard image
New cards
74

x+c

knowt flashcard image
New cards
75

sin(x)+C

knowt flashcard image
New cards
76

-cos(x)+C

knowt flashcard image
New cards
77

tan(x)+C

knowt flashcard image
New cards
78

-cot(x)+C

knowt flashcard image
New cards
79

sec(x)+C

knowt flashcard image
New cards
80

-csc(x)+C

knowt flashcard image
New cards
81

Fundamental Theorem of Calculus #1

The definite integral of a rate of change is the total change in the original function.

<p>The definite integral of a rate of change is the total change in the original function.</p>
New cards
82

Fundamental Theorem of Calculus #2

knowt flashcard image
New cards
83

Mean Value Theorem for integrals or the average value of a functions

knowt flashcard image
New cards
84

ln(x)+C

knowt flashcard image
New cards
85

-ln(cosx)+C = ln(secx)+C

hint: tanu = sinu/cosu

<p>hint: tanu = sinu/cosu</p>
New cards
86

ln(sinx)+C = -ln(cscx)+C

knowt flashcard image
New cards
87

ln(secx+tanx)+C = -ln(secx-tanx)+C

knowt flashcard image
New cards
88

ln(cscx+cotx)+C = -ln(cscx-cotx)+C

knowt flashcard image
New cards
89

If f and g are inverses of each other, g'(x)

knowt flashcard image
New cards
90

Exponential growth (use N= )

knowt flashcard image
New cards
91

Formula for Disk Method

Axis of rotation is a boundary of the region.

<p>Axis of rotation is a boundary of the region.</p>
New cards
92

Formula for Washer Method

Axis of rotation is not a boundary of the region.

<p>Axis of rotation is not a boundary of the region.</p>
New cards
93

Inverse Secant Antiderivative

knowt flashcard image
New cards
94

Inverse Sine Antiderivative

knowt flashcard image
New cards
95

Derivative of eⁿ

knowt flashcard image
New cards
96

ln(a)*aⁿ+C

knowt flashcard image
New cards
97

Derivative of ln(u)

knowt flashcard image
New cards
98

Antiderivative of f(x) from [a,b]

knowt flashcard image
New cards

Explore top notes

note Note
studied byStudied by 92 people
... ago
5.0(1)
note Note
studied byStudied by 62 people
... ago
5.0(4)
note Note
studied byStudied by 18 people
... ago
5.0(1)
note Note
studied byStudied by 20 people
... ago
5.0(1)
note Note
studied byStudied by 18 people
... ago
5.0(1)
note Note
studied byStudied by 23 people
... ago
5.0(1)
note Note
studied byStudied by 5 people
... ago
5.0(1)
note Note
studied byStudied by 648 people
... ago
5.0(2)

Explore top flashcards

flashcards Flashcard (55)
studied byStudied by 16 people
... ago
5.0(1)
flashcards Flashcard (109)
studied byStudied by 10 people
... ago
4.4(5)
flashcards Flashcard (42)
studied byStudied by 9 people
... ago
5.0(1)
flashcards Flashcard (20)
studied byStudied by 9 people
... ago
5.0(1)
flashcards Flashcard (30)
studied byStudied by 457 people
... ago
5.0(3)
flashcards Flashcard (80)
studied byStudied by 2 people
... ago
5.0(2)
flashcards Flashcard (231)
studied byStudied by 27 people
... ago
5.0(1)
robot