Integral Applications Flashcards
1
Q
Cross Sections
-The volume would be the sum of the cross sectional areas times _.
A
Height
2
Q
Mean Value Theorem for Integrals
- f(x) is continuos on [a,b]
- Then there exists some member c such that a <= c <= b and fâ(c) = [f(b) - f(a)] / (b - a) = _ = [S(ab)fâ(x)dx] / (b - a) = _
A
Slope, average
3
Q
_ Method
- A = pi( f(x) )^2 - pi( g(x) )^2
- V = S(ab) pi( f(x)^2 - g(x)^2 )dx
A
Washer
4
Q
Area of Isosceles Triangle
A
(1/4)h^2
5
Q
Cross Sectional Area Perpendicular to Y Axis
- =
- _ = _1 , _2
- _ - _
- S(_12) V( _ - _ )d
A
y, right, left
6
Q
Cross Sectional Area Perpendicular to X Axis
- =
- _ = _1 , _2
- _ - _
- S(_12) V( _ - _ )d
A
x, top, bottom
7
Q
Motion
- Sa(t)dt = _ = antiderivative (+c)
- Plug in numbers where applicable
- Sv(t)dt = _ = antiderivative (+c)
- Plug in numbers where applicable
A
v(t), s(t)
8
Q
Vertical Disk
- around x=
- S(_12) [ pi ( _ - _ )^2 ]d
A
y, right, left
9
Q
Horizontal Disk
- around y=
- S(_12) [ pi ( _ - _ )^2 ]d
A
x, top, bottom
10
Q
Disk X Axis
- =
- _ = _1 , _2
- V = pir^2h
- S(_12)[ pi ( _ - _ )^2 ]d
A
x, top, bottom
11
Q
Disk Y Axis
- =
- _ = _1 , _2
- V = pir^2h
- S(_12)[ pi ( _ - _ )^2 ]d
A
y, right, left
12
Q
Area of Equilateral Triangle
A
(sqt(3)/4)h^2
13
Q
Three Line Area
-area1 + area 2 = _ + _
A
S(ab)f(x)dx, S(bc)f(x)dx
14
Q
Displacement
- Velocity
- _
A
S(t1t2)v(t)dt
15
Q
Distance
- Speed
- _
A
S(t1t2) | v(t) | dt
