fuck it we ball
k² - x²
x = ksinθ
x² + k²
x = ktanθ
x² - k²
x = ksecθ
a odd
u = sin x
b odd
u = cosx
-(a+b) even
u = tanx
integral of b^x
b^x / (lnb)
error bound formula midpoint rule
K(b-a)³/(24n²)
error bound trapezoidal rule
K(b-a)³/(12n²)
error bound formula simpsons rule
K(b-a)^5/(180n²)
IBP
int uv’ = uv - int u’v
double angle identity (sin2θ = ?)
2cosθsinθ
x²-1
quadratic
x+1
constant
x
constant
x²
constant
(x+1)²
constant
(x²-1)²
quadratic
concave up on [a,b]
Mn < f(x) < Tn
concave down on [a,b]
Tn < f(x) < Mn
increasing on [a,b]
Ln < f(x) < Rn
decreasing on [a,b]
Rn < f(x) < Ln