Formulas Flashcards
Arc-length formula
Integral from “a” to “b” of root 1 plus y’^2 dx.
Midpoint Rule
(b-a)/n[f(x)+f(x)+f(n)]
Trapezoid Rule
deltaX/2 [f(x)+2f(x)+2f(x)+f(n)]
(b-a)/2)/3[f(x)+4f(x)+2f(x)+4f(x)+f(n)]
Simpson’s Rule
Trapezoid Error Bound
|Et|
Midpoint Error Bound
|Em|
Simpson’s Error Bound
|Es|
Integral from a to b of 2pi r times arc length.
Surface Area
2pi•r•h dr.
Volume
1/(b-a)integral a to b f(x)dx
Mean Value Theorem (find the middle value of a function)
Sigma (x)^n
1/(1-x), series of;
Sigma x^n/n!
e^x, series of;
Sigma (-1)^n x^2n+1/(2n+1)!
Sin(x), series of;
Sigma (-1)^n x^2n/(2n)!
Cos(x), series of;
Sigma (-1)^n x^2n+1/(2n+1)
Arctan(x), series of;
Sigma n=1 (-1)^n-1 x^n/n
Ln(1+x)
Sigma(k n) x^n. 1+kx+k(k-1)•z^2/2!
(1+x)^k, series of;
Washer Formula
Integral pi(L radius^2 - s radius^2) dx
Work of water tank
Density•gravity(9800) Integral £area•distance traveled by each slice dx.
