all of the formulas

oh yeah baby it's formula time

∑a*rⁿ

geometric series

∑1/pⁿ

p-series

a_n(x-c)ⁿ/n!

taylor series

a_n(x)ⁿ/n!

maclaurin series

lim→|a_n+1/a_n|

ratio test

conditions for integral test

positive, decreasing, continuous

1/-√1-x²

sin^-1x

1/1+x²

tan^-1x

1/|x|√x²-1

sec^-1x

1/2(b₁+b₂)Δx

area of a trapezoid

d/dx tanx

sec²x

d/dx cotx

-csc²x

d/dx secx

secxtanx

d/dx cscx

-cscxcotx

uv-∫vdu

integration by parts

∫√1+f’(x)²dx

arc length of a curve

∫(f(x)-g(x))dx

area between curves

∫(f(x)-g(x))²dx

area with square cross sections

1/8π∫(f(x)-g(x))²dx

area with semicircle cross sections

1/2∫(f(x)-g(x))²dx

area with right isosceles triangle cross sections

√3/4∫(f(x)-g(x))²dx

area with equilateral triangle cross sections

π∫r(x)²dx

volume by disc revolution

π∫f(x)²-g(x)²dx

volume by washer revolution

KP(1-P/M) or K/M*P(M-P)

logistic formulas

∫√x’(t)²+y’(t)²dt

arc length of a parametric/total distance travelled for a vector

√x’(t)²+y’(t)²

speed formula for vector

1/2∫r²dθ

area of a polar curve

∫√r²+r’²dθ

arc length of a polar curve

1/b-a∫f(x)dx

average value

x_n-1+h; y_n-1+hf’(x_n-1,y_n-1)

euler’s method

rcosθ

x term in a polar function

rsinθ

y term in a polar function