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Integartion
Integartion
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1
Integration techniques
2sin(x)+2xcos(x)
2xcos(x)-x2sin(x)
x2cos(x)
x2sin(x)
2
Integration
-1/2
1
2 ln2
1/2
3
T or F: Transpiration happens at the same time as Integration
True
False
4
How many domains of integration are there?
Eight
Three
Thirteen
Seven
5
What is the integration formula for: ∫
kdx
=
kx + c
kx + a
kx + d
kx + b
6
Horizontal Integration does What?
Grants us "Mindsight" (This is technically correct but not).
Allows for the un-blocking of the two sides of our Brain.
Dunder Mifflin downsizing
Allows us to co-exist with others
7
The second fundamental theorem of calculus states that...
F'(x)=f(x)
F(B)-F(A)
F(t)=G(t)
x
8
Integration 5: Integrate the following.
((2x - 5)11 / 11)+ C
((2x - 5)11 / 22)+ C
((2x + 5)11 / 22)+ C
((2x - 5)12 / 12)+ C
9
Which integration technique would you use on this function?
integration by parts
Power rule
U sub
Reverse chain rule
10
Change the limit of integration
[e,1]
[e,0]
[1,e]
[0,e]
11
Using the chain rule of integration, what is the integral of:
y=n(x+a)n+1+c
y=((1-(n-1))(x+a)n+1+c
y=n(x+a)n-1+c
y=((1/(n+1))(x+a)n+1+c
12
Which technique of integration is pictured below?
Partial Fractions
Integration by Parts
Product Rule
u Substitution
13
Does integration use the power rule?
No
Yes
maybe
14
What is the correct integration?
x
Ln IxI
Ln lxl +C
Ln x+C
15
The first theorem of calculus is
Mental torture, dude
The value of the hypotenuse
A method to calculate square roots
The area below the curve
16
How is integration related to derivatives
they are the same thing
derivatives come after integration
integration is reverse derevatives
integration is not related to derivatives
17
Integration 4: Integrate the following.
(1/10)sin(5x2) + C
(-1/10)sin(5x2) + C
(1/10)cos(5x2) + C
(1/25)sin(5x2) + C
18
Integration
x3 - x
6x - 12
3x2 - 12
x3 - x - 6
19
Integration 1: Find the area under the curve.
500
1050
550
1550
20
"When ____ happens, integration cannot occur."
Excitement or Extreme Emotion
Anxiety
Differentiation
Calculus Derivatives
21
What is the formula for Integration by Parts?
∫u dv= u-v du
∫u dv= v-v du
∫u dv= v-u dv
∫u dv= uv-v du
22
Integration
16/9
6
3
2
23
Use calculus to solve this problem:
2
0
5
-4
24
What is the correct integration?
3x+C
3x^2
-3x^2+C
3x^2+C
25
Integration 2: Find the
displacement
traveled
1550
500
1000
550
26
Which of the following integration rules is correct?
∫(secxtanx)dx = cscx + C
None of these
∫k dx = k + C
∫0dx = C
27
Integration
sec(x) + C
sec2(x)/2 + C
tan(x) + C
tan2(x)/2 + C
28
Indefinite Integration Problem (no calculator)
-1
1
0
-π
29
Solve the limit of integration
0
π/2
π
2π
30
Solve the limit of integration
earctan(e)-1
-1
e-1
tan-19(e)
31
Integration
tan x + C
csc2x + C
cos2x + C
2 sec2x tan x + C
32
What is the integral if using exponential integration?
y=ex+c
y=xex-1+c
y=((ex+1)/(x+1))+c
y=x+c
33
Solve the limit of integration
7
(11/3)-((20√(10))/3)
(11/3)=((20√(10))/3)
11+(20√(10))
34
Integration 3: Integrate the following function.
(1/3)ln|x3 + 4| + C
ln|x3 + 4|
ln|x3 + 4| + C
(1/3x2)ln|x3 + 4| + C
