Calculus 2 Exam 2 Flash Cards

Front 1

a = ∫(f(x)-g(x),x,a,b)

Back 1

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)

Front 2

a = ∫(g(t)f˙(t),t,c,d)

Back 2

Areas Between Curves

This equation is used for parametric curves. In the equation x = f(t) and y = g(t)

Front 3

v = ∫(A(x),x,a,b)

Back 3

Volumes

This equation finds a volume with respect to x. This means that x is sliced perpendicular.

Front 4

v = ∫(A(y),y,c,d)

Back 4

Volumes

This equation finds a volume with respect to y. This means that y is sliced perpendicular.

Front 5

A = π(r)^2

Back 5

Volumes

The volume of a disk

Front 6

A = π(outer radius)^2 - π(inner radius)^2

Back 6

Volumes

The volume of a washer

Front 7

r^2 = (x-h)^2 + (y-k)^2

Back 7

Volumes

The equation of a circle

Front 8

y = kx^2

Back 8

Volumes

The equation of a parabola

Front 9

L = ∫(√((dx/dt)^2 + (dy/dt)^2)),t,a,b)

Back 9

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)

Front 10

L = ∫(√(1=(dy/dx)^2),x,a,b)

Back 10

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)

Front 11

L = ∫(√((dx/dy)^2+1),y,a,b)

Back 11

Arc Length

This equation is used when finding the length given x = f(y).

Front 12

Fave = (1/(b-a) ∫(f(x),x,a,b)

Back 12

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.

Front 13

∫(f(x),x,a,b) = f(c)(b-a)

Back 13

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.

Front 14

w = lim(n->inf)∑(f(x)∆x,i=1,n) = ∫(f(x),x,a,b)

Back 14

Applications to Physics and Eng.

This equation is used to find the work moving a object from a to b

Front 15

f(x) = kx

Back 15

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.

Front 16

My = ∂∫(x*f(x),x,a,b)

Back 16

Applications to Physics and Eng.

This equation finds the moment about the y axis.

Front 17

Mx = ∂∫((1/2)f(x)^2,x,a,b)

Back 17

Applications to Physics and Eng.

This equation finds the moment about the x axis.

Front 18

m(x hat) = My

Back 18

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

Front 19

m(y hat) = Mx

Back 19

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

Front 20

(x hat) = My/m

Back 20

Applications to Physics and Eng.

This equation is a way to solve for the x coordinate of the centroid.

Front 21

(y hat) = Mx/m

Back 21

Applications to Physics and Eng.

This equation gives a way to solve for the y coordinate of the centroid using M_ and m.

Front 22

m = ∂A = ∂∫f(x),x,a,b)

Back 22

Applications to Physics and Eng.

This is the equation (multiple equations) to find the mass of a area.

Front 23

(x hat) = 1/A * ∫(xf(x),x,a,b)

Back 23

Applications to Physics and Eng.

This equation finds the x coordinate of the centroid.

Front 24

(y hat) = 1/A * ∫((1/2)f(x)^2,x,a,b)

Back 24

Applications to Physics and Eng.

This equation finds the y coordinate of the centroid.