AP Calc-integrals

studied byStudied by 32 people
5.0(1)
Get a hint
Hint

∫du

1 / 41

flashcard set

Earn XP

Description and Tags

42 Terms

1

∫du

u + C

New cards
2

∫edu

e^u + C

New cards
3

∫cos(u)du

sin(u) + C

New cards
4

∫cot(u)du

lnIsin(u)I + C

New cards
5

∫csc(u)du

-lnIcsc(u) + cot(u)I + C

New cards
6

∫csc²(u)du

-cot(u) + C

New cards
7

∫csc(u)cot(u)du

-csc(u) + C

New cards
8

∫du/(a²+u²)

(1/a)arctan(u/a) + C

New cards
9

∫[f(u) + g(u)]du

∫f(u)du + ∫g(u)du

New cards
10

∫[f(u) - g(u)]du

∫f(u)du - ∫g(u)du

New cards
11

∫(a^u)du

(1/ln(a))a^u +C

New cards
12

∫sin(u)du

-cos(u) + C

New cards
13

∫tan(u)du

-lnIcos(u)I + C

New cards
14

∫sec(u)du

lnIsec(u) + tan(u)I + C

New cards
15

∫sec²(u)du

tan(u) + C

New cards
16

∫sec(u)tan(u)du

sec(u) + C

New cards
17

∫du/√(a²-u²)

arcsin(u/a) +C

New cards
18

∫du/[(u)√(u²−a²)

(1/a)arcsec(IuI/a) + C

New cards
19

net change formula

∫f'(x)=f(b) - f(a)

New cards
20

when do you use net change formula?

when the question asks for a rate of change

New cards
21

∆x=?

(b-a)/n

New cards
22

xi=

a + i∆x

New cards
23

area under the curve=

∆x(∑heights)

New cards
24

trapezoidal rule

(b-a)/(2n)[f(a) + 2f(n-1) + f(b)]

New cards
25

how do you do a midpoint sum

you take the ∆x of the points and multiply it by the middle number

New cards
26

∑c=

cn

New cards
27

n(n+2)/2

New cards
28

∑i²=

n(n+1)(2n+1)/6

New cards
29

∑i³=

n²(n+1)²/4

New cards
30

∑(ai + bi)=

∑ai + ∑bi

New cards
31

∫f(x)dx=

limn→∞∑f(xi)∆x

New cards
32

(d/dx)g(x)=∫(from x to 0)√1+t² dt(d/dx)=

g'(x)=√1+x² (1) - √1+0² (0)

New cards
33

∫x^n=

(x^n+1)/(n+1)

New cards
34

∫(from a to a)f(x)dx=

0

New cards
35

∫(from b to a)f(x)dx=

-∫(from a to b)f(x)dx

New cards
36

f(avg)=

1/(b-a)∫(from a to b)f(x)dx

New cards
37

steps for u-sub

  1. choose u

  2. find du

  3. rewrite integral in terms of u

  4. evaluate integral

  5. replace u with function

New cards
38

if f is even, f(-x)=f(x), then ∫(from -a to a)f(x)dx=

2∫(from 0 to a)f(x)dx

New cards
39

if f is odd, f(-x)=-f(x), then ∫(from -a to a)f(x)dx=

0

New cards
40

when n/d, n is 2 less, use...

inverse trig

New cards
41

when n/d, n=d, use...

u-sub

New cards
42

when n/d, n≥d, use...

long division

New cards

Explore top notes

note Note
studied byStudied by 114 people
... ago
5.0(2)
note Note
studied byStudied by 15 people
... ago
5.0(1)
note Note
studied byStudied by 20 people
... ago
5.0(2)
note Note
studied byStudied by 72 people
... ago
5.0(1)
note Note
studied byStudied by 64 people
... ago
5.0(2)
note Note
studied byStudied by 37 people
... ago
5.0(2)
note Note
studied byStudied by 94 people
... ago
5.0(1)
note Note
studied byStudied by 9241 people
... ago
4.8(73)

Explore top flashcards

flashcards Flashcard (33)
studied byStudied by 2 people
... ago
5.0(1)
flashcards Flashcard (149)
studied byStudied by 14 people
... ago
5.0(1)
flashcards Flashcard (30)
studied byStudied by 4 people
... ago
5.0(1)
flashcards Flashcard (37)
studied byStudied by 17 people
... ago
5.0(1)
flashcards Flashcard (30)
studied byStudied by 2 people
... ago
4.5(2)
flashcards Flashcard (21)
studied byStudied by 8 people
... ago
5.0(1)
flashcards Flashcard (111)
studied byStudied by 29 people
... ago
5.0(1)
flashcards Flashcard (162)
studied byStudied by 17 people
... ago
5.0(1)
robot