Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
24 Cards in this Set
- Front
- Back
a = ∫(f(x)-g(x),x,a,b)
|
Areas Between Curves
This equation finds the area of a curve bounded by a and b and above by f(x), below by g(x) |
|
a = ∫(g(t)f˙(t),t,c,d)
|
Areas Between Curves
This equation is used for parametric curves. In the equation x = f(t) and y = g(t) |
|
v = ∫(A(x),x,a,b)
|
Volumes
This equation finds a volume with respect to x. This means that x is sliced perpendicular. |
|
v = ∫(A(y),y,c,d)
|
Volumes
This equation finds a volume with respect to y. This means that y is sliced perpendicular. |
|
A = π(r)^2
|
Volumes
The volume of a disk |
|
A = π(outer radius)^2 - π(inner radius)^2
|
Volumes
The volume of a washer |
|
r^2 = (x-h)^2 + (y-k)^2
|
Volumes
The equation of a circle |
|
y = kx^2
|
Volumes
The equation of a parabola |
|
L = ∫(√((dx/dt)^2 + (dy/dt)^2)),t,a,b)
|
Arc Length
This is the equation to find the length of a parametric curve between a and b with x = f(t) and y = g(t) |
|
L = ∫(√(1=(dy/dx)^2),x,a,b)
|
Arc Length
The is the equation to find the length of a curve with given y = f(x). Regard x as a parameter and set the parametric equation equal to x=x and y=f(x) |
|
L = ∫(√((dx/dy)^2+1),y,a,b)
|
Arc Length
This equation is used when finding the length given x = f(y). |
|
Fave = (1/(b-a) ∫(f(x),x,a,b)
|
Average Value
(1) This finds a average value of a function between a and b. It uses the mean value theorem. The function must be continuos. |
|
∫(f(x),x,a,b) = f(c)(b-a)
|
Average Value
(2) This finds a average value of a function between a and b. It uses the mean value theorem. The function must be continuos. |
|
w = lim(n->inf)∑(f(x)∆x,i=1,n) = ∫(f(x),x,a,b)
|
Applications to Physics and Eng.
This equation is used to find the work moving a object from a to b |
|
f(x) = kx
|
Applications to Physics and Eng.
This is called Hookes Law. Y = newtons, x=displacement and k = spring constant (different for each spring). The spring function can be integrated to find work from a distance. SI unit is ft-lb. |
|
My = ∂∫(x*f(x),x,a,b)
|
Applications to Physics and Eng.
This equation finds the moment about the y axis. |
|
Mx = ∂∫((1/2)f(x)^2,x,a,b)
|
Applications to Physics and Eng.
This equation finds the moment about the x axis. |
|
m(x hat) = My
|
Applications to Physics and Eng.
This equation sets a basic relationship between the mass, the x coordinate of the centroid and the moment around the _ axis |
|
m(y hat) = Mx
|
Applications to Physics and Eng.
This equation sets a basic relationship between the mass, the y coordinate of the centroid and the moment around the _ axis |
|
(x hat) = My/m
|
Applications to Physics and Eng.
This equation is a way to solve for the x coordinate of the centroid. |
|
(y hat) = Mx/m
|
Applications to Physics and Eng.
This equation gives a way to solve for the y coordinate of the centroid using M_ and m. |
|
m = ∂A = ∂∫f(x),x,a,b)
|
Applications to Physics and Eng.
This is the equation (multiple equations) to find the mass of a area. |
|
(x hat) = 1/A * ∫(xf(x),x,a,b)
|
Applications to Physics and Eng.
This equation finds the x coordinate of the centroid. |
|
(y hat) = 1/A * ∫((1/2)f(x)^2,x,a,b)
|
Applications to Physics and Eng.
This equation finds the y coordinate of the centroid. |