## Glossary of Calculus 2 2

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- What is the arc length formula?
- ∫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*)]Δx

W = lim(n->∞) Σ{[(xi*)2 + 2(xi*)]Δx}

W = ∫(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

- What is My in the following problem? Find the moments and center of mass of the system of objects that have masses 3,4,8 @ (-1,1),(2,-1), and (3,2)
- My = 3(-1) + 4(2) + 8(3)

- What is Mx in the following problem? Find the moments and center of mass of the system of objects that have masses 3,4,8 @ (-1,1),(2,-1), and (3,2)
- Mx = 3(1) + 4(-1) + 8(2)

- 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?
- [∫(x*f(x))dx]/[∫f(x)dx]

- What's the formula for the y value of a center of mass on a lamina?
- [∫0.5*(f(x))^2dx]/[∫f(x)dx]

- What does not matter when finding centers of mass?
- DENSITY!