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