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Integral Calculus Flashcards

1
Q

True or false, indefinite integral has limits

A

False

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2
Q

∫ a du =

A

a ∫ du = au + c

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3
Q

∫ a^u du =

A

a^ u / In a + c , a > 1, a=1

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4
Q

∫ u^n du

A

= 1/ n +1 u^n+1

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5
Q

∫e^u du

A

= e^u + C

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6
Q

∫ u^-1 du

A

= du/u = ln abs u + c

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7
Q

∫ln u du

A

=u ln abs u - u +c

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8
Q

∫ sin u

A

= -cos u+ c

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9
Q

∫ cos u du

A

= sin u + c

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10
Q

∫ tan u du

A

= ln abs sec u + c

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11
Q

∫ cot u du

A

= ln abs sin u + c

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12
Q

∫ sec u du

A

= ln abs sec u + tan u + c

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13
Q

∫csc u du

A

= ln |csc u - cot u| + c
= - ln |csc u - cot u| + c

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14
Q

∫ sec u tan u du

A

= sec u + c

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15
Q

∫csc u cot u du

A

= - csc u + c

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16
Q

∫sec^2 u du

A

= tan u+ C

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17
Q

∫csc^2 u du

A

= -cot u + c

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18
Q

Indefinite Integral caltech

A
  1. Input given, let x be any uncommon number
  2. Differentiate all choices usng d/dx function in calcu, let x be same in step 1
  3. Which ever is the same in step 1 is the answer
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19
Q

Integral by parts caltech

A

Differentiate u and v till zero, see notes for full step

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20
Q

Plane Areas: Vertical Strip Formula

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21
Q

Plane Areas: Horizontal Strip Formula

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22
Q

Plane Areas: Radial Strip Formula

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23
Q

Plane areas: Step in solving rectangular strip

A
  1. Plot the given curve
  2. Choose what strip to use
  3. Solve for the equation to be integrated (Xr-Xl) or (Yu-Yl)
  4. Find the limits (POI), equate the two equations solved from step 3
24
Q

Plane areas: Step in solving radial strip

A
  1. Make equation equal to r
  2. Substitute r to radial strip formula
  3. Get limits using mode 6 (table)
    Start: 0, End: 2pi, Step: pi/12
25
Area of some polar curve: r2 = k cos 2 theta
Area= K [link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
26
Area of some polar curve: r2 = k sin 2 theta
Area= K [link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
27
Area of some polar curve: r2 = k sin theta
Area= 2K [link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
28
Area of some polar curve: r2 = k cos theta
Area= 2K [link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
29
Area of some polar curve: r = k(1+cos theta)
Area = 1.5 pi K^2 Perimeter = 2pi a [link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
30
Area of some polar curve: r = k(1+sin theta)
Area = 1.5 pi K^2 Perimeter = 2 pi a [link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
31
Area of some polar curve: r = k sin 3 theta
Area = 1/4 pi k^2 [link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
32
Area of some polar curve: r = k cos 3 theta
Area = 1/4 pi k^2 [link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
33
Area of some polar curve: r = k cos 2 theta
Area = 1/2 pi k^2 [link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
34
Area of some polar curve: r = 2 k cos theta
Area = pi k^2 [link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
35
Area of some polar curve: r = 2 k sin theta
Area = pi k^2 [link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
36
Volume of Solid of Revolution: Disk method formula
[link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
37
In disk method: the orientation of the strip must be ______ to the axis of revolution
perpendicular
38
Volume of Solid of Revolution: Disk method formula
[link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
39
In ring method: the orientation of the strip must be ______ to the axis of revolution
perpendicular
40
Volume of Solid of Revolution: Shell method formula
[link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
41
Second Proposition of Pappus, what method and formula
Shell Method V = 2pi A d
42
Length of Curves: Parametric Formula
[link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
43
Length of Curves: Rectangular Formula
[link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
44
Length of Curves: Polar Formula
[link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
45
First Proposition of Pappus, what method and formula
Surface area of Curves SA = 2 pi integral of d.ds
46
First Moment of Area
Centroid
47
Centroid Formula
[link to formula](https://drive.google.com/file/d/15DTcnGslisKr_Q1jZvQCPRtYLLCPbY5M/view?usp=sharing)
48
Second Moment of Area
Moment of Inertia
49
Moment of Inertia resists:
bending
50
Moment of Inertia: y- axis
Iy = integral of x^2 dA or Iy = 1/3 integral of x^3 dy
51
Moment of Inertia: x- axis
Ix = integral of y^2 dA or Ix = 1/3 integral of y^3 dx
52
Moment of Inertia: differential area must be _______ to the "with respect of x/y axis"
Parallel
53
Polar Moment of Inertia Formula
J= R^2 dA or J= Iy + Ix
54
Product of Inertia Formula
Ixy = integral of xy dA
55
Work Problems
Work = integral of f(x) . dX

MSTE (7 decks)

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