Unit Six: Integration and Accumulation of Change
0.0(0)
Studied by 6 people0%Exam Mastery
Build your Mastery score
AP PracticeSupplemental Materials
Call Kai
Call KaiCard Sorting
1/39
Earn XP
Description and Tags
Last updated 10:28 PM on 12/8/22
Name | Mastery | Learn | Test | Matching | Spaced | Call with Kai |
|---|
No analytics yet
Send a link to your students to track their progress
40 Terms
1
New cards
Integral of cf(x)dx
c integral f(x)dx
2
New cards
Integral from a to b f(x)dx
-(negative) integral from b to a f(x)dx
3
New cards
integral from a to c f(x)dx
integral from a to b f(x)dx + integral from b to c f(x)dx
4
New cards
integral from a to a f(x)dx
0
5
New cards
integral from a to b -f(x)dx
-(negative) integral from a to b f(x)dx
6
New cards
Integral of (f(x)+g(x))dx
integral f(x)dx + integral g(x)dx
7
New cards
Fundamental Theorem of Calculus
∫ f(x) dx on interval a to b = F(b) - F(a)
8
New cards
Integral from a to b of c
cx|(a to b)
9
New cards
integral from a to b of cxˆn
cxˆ(n+1)/n+1 |(a to b)
10
New cards
integral from a to b 1/xdx
ln|x| |(a to b)
11
New cards
integral of sinx dx
-cosx + c
12
New cards
integral of secˆ2x dx
tanx + c
13
New cards
Integral of cscxcotx dx
-cscx + C
14
New cards
integral of cosx dx
sinx + c
15
New cards
integral of cscˆ2x dx
-cotx + c
16
New cards
integral of secxtanx dx
secx + c
17
New cards
integral of e^x dx
e^x + c
18
New cards
integral of eˆ5x dx
1/5 eˆ(5x) + c
19
New cards
Riemann Sum
lim n -> ∞ Σ k = 1 to n f(xk*) • Δx
20
New cards
lim n -> ∞ Σ k = 1 to n f(xk*) • Δx
lim n -> ∞ Σ k = 1 to n f(a+k((b-a)/n)) • (b-a)/n
21
New cards
xk*
a+kΔx
22
New cards
Δx
(b-a)/n
23
New cards
Fundamental theorem of calculus (derivative)
d/dx F(x)= d/dx integral from a to x f(t) dt = f(x)
24
New cards
When dealing with fundamental theorem of calc. (derivative) and the x is different (such as xˆ2), use
Chain rule
25
New cards
Displacement
Integrate velocity
26
New cards
Integral from a to b of v(t) dt
27
New cards
Total distance traveled
Integrate speed
28
New cards
Integral from a to b of |v(t)| dt
29
New cards
Displacement
How much you moved from starting position
30
New cards
Acceleration
Derivative of velocity
31
New cards
Position
Antiderivative of velocity
32
New cards
Average value theorem
1/b-a integral from a to b of f(x) dx
33
New cards
F(x) is inc. then LRAM will be an
Underapproximation (LRAM)
34
New cards
F(x) is Dec. then LRAM will be an
Overestimate (LRAM)
35
New cards
F(x) is inc. then RRAM will be an
Overestimate (RRAM)
36
New cards
F(x) is Dec. then RRAM will be an
Underestimate (RRAM)
37
New cards
F(x) is ccd. then MRAM will be an
Overestimate (MRAM)
38
New cards
F(x) is ccu. then MRAM will be an
Underestimate (MRAM)
39
New cards
F(x) is ccd. then TAM will be an
Underestimate (TAM)
40
New cards
F(x) is ccu. then TAM will be an
Overestimate (TAM)