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Applications of Integrals
Calculating using integrals (from AP Calc BC / College Calc II)
12
Mathematics
12th Grade
01/22/2012

Additional Mathematics Flashcards

 


 

Cards

Term
Standard Area
Definition
∫ab f(x) - g(x) dx
Term
Washer Method
Definition

π∫ab (f(x)-k)2 - (g(x) - k)2 dx


Around the line y = k

 

 

Term
Shell Method
Definition

2π∫ab |x-h|*(f(x)-g(x)) dx


Around the line x = h

 

 

Term

Finding Centroid

_  _

(x, y)

Definition

( ∫ab x*(f(x)-g(x))dx

 

∫ab (f(x)-g(x)) dx

,

.5 ∫ab f(x)2 - g(x)2 dx

 ∫ab (f(x)-g(x)) dx )

 
 

 

Term
Arc Length
Definition
∫ab √(1 + f'(x)2)
Term

Hanging Chain

(Work)

Definition

∫0L (L-y)*(m*g)/L dy

Term

Spring

(Work)

Definition

∫ab kx dx


k = spring constant

 

 

Term

Leaky Bucket

(Work)

Definition

∫if (mog - Rt) * x/Δt dt


i, f = initial/final time
R = leak rate
Δt = f - i
i usually = 0

 

Term

Pumping Liquid

(Work)

Definition

ρg ∫ab (H-y) A(y) dy


ρg = weight density
A(y) = area of cross-section  |  to y

 

 

Term
Force due to Pressure
Definition

ρg∫ab (H-y)*L(y) dy


H = total height of plate

L(y) = length of plate at y

 

 

 

 

Term

MVT for Integrals

(Average value on [a, b])

Definition
1/(b-a) * ∫ab f(x) dx
Term
Volume by Slicing
Definition

∫ab A(x) dx


A(x) = area of cross-section

 

 

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