# Calculus 2 2

## Terms

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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!

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