Calc 2 Material

ln(xy) =

lnx + lny

ln(xP) =

Plnx

ln(e^x²) =

x²

Population Formula

p(t) = Pe^rt

Cross Sectional Area Formula

A(x) = π(2rx-x²)

Work formula for cross sectional area

W = ∫(p)(x)(A(x))dx

Area under a curve

Just evaluate the intergral

Area of a region formula

A = ∫(top-bottom)dx

How do you find the top vs bottom function?

Set the 2 X’s equal to eachother to find the intersection.

Volume of a solid (x- axis)

V =π ∫(outer²-inner²)dx

simpsons rule

∫f(x)dx = 1/3(b - a / n) [f(x0) + 4f(x1) + 2f(x2) + 4f(x3) +f(xn)]

Arc Length formula

L = ∫sqrt[1+(df/dx)²dx]

Hookes Law

F=kx

Work for spring

w = ∫kxdx

X coordinate for center of mass

xHat = 1/A∫xf(x)dx

A =

∫fxdx

Y coordinate for center of mass

yHat = 1/2A∫f(x)²dx

Mass of Wire

m = ∫f(x)dx

Moment

M = ∫ x(f(x))dx

Xhat

M/m (moment over mass)

Hydrostatic force

F = ∫ p(g)(depth)(width at depth y)

McLaurin Series

idk lol