Calculus 2 2
Terms
undefined, object
copy deck
 What is the arc length formula?
 âˆ«sqrt[((d/dx)y)^2+((d/dx)x)^2]dt on a to b.
 When doing area, volume, and arc length, x ALWAYS GOES WITH ____ when finding the boundaries?
 X!!!!

If we have y = x^2 + 2x, what can we use for y in the arc length formula on (0,1) to (4,5)?
What are a and b in the integral? 
We can use 1 for y.
a and b are 0 and 4.  A particle is located x ft. from the origin, a force of x^2+2x lbs. acts on it. How much work is done in moving it from x=1 to x=3? WRITE OUT

Fi = [(xi*)2 + 2(xi*)]
Wi = [(xi*)2 + 2(xi*)]Î”x
W = lim(n>âˆž) Î£{[(xi*)2 + 2(xi*)]Î”x}
W = âˆ«(x^2+2x)dx from 1 to 3.  What's the formula for mass?
 Mass = density*volume
 What's the density of water?

1000 kg/m^3
or
1 g/cm^3
or
62.5 lb./ft^3  What is the formula for pressure?

P = ρgd
ρ = density
g = gravity
d = depth  What is the formula for hydrostatic force?
 Hydrostatic Force = Pi*Ai
 What are the units for pressure?
 Pascals
 Once you've calculuated Mx and My, what do you do?
 Divide both by the mass. So your interval is from (My/m,Mx/m)
 What's the formula for the x value of a center of mass on a lamina?
 [âˆ«(x*f(x))dx]/[âˆ«f(x)dx]
 What's the formula for the y value of a center of mass on a lamina?
 [âˆ«0.5*(f(x))^2dx]/[âˆ«f(x)dx]
 What does not matter when finding centers of mass?
 DENSITY!