Newton's Method, Antiderivatives, Indefinite Integrals

Front 1

Newton's Method

Back 1

x'sub'n+1 = xn - [ f (xn) / f '(xn) ]

remark: it is used as an iterative process which locates roots of functions
graphically: roots are x coordinate intercepts of a function

Front 2

antiderivative - definition

Back 2

A function F is called an antiderivative of f on an interval I if F '(x) = f (x) for all x in I.

Front 3

General Antiderivative (with constant) - definition

Back 3

If F is an antiderivative of f on an interval I, then the most general antiderivative of f on I is
F(x) + C
Where C is an arbitrary constant.

Corollary: If f '(x) = g '(x) for all x in interval (a, b) then f(x) = g(x) + C where C is some constant

Front 4

Indefinite Integral - definition

Back 4

∫ f(x)dx = F(x) + C

∫ - indefinite integral
f(x) - integrand
dx - differential
F(x) - general antiderivative of f(x)

Front 5

Indefinite Integral Formula
∫ cf(x)dx =

Back 5

c∫ f(x)dx

Front 6

Indefinite Integral Formula
∫ kdx =

Back 6

kx + C

Front 7

Indefinite Integral Formula
∫ [f(x) + g(x)]dx =

Back 7

∫ f(x)dx + ∫ g(x)dx

Front 8

Indefinite Integral Formula
∫ x^n dx =

Back 8

[(x^(n+1))/(n+1)] + C
n ≠ -1

Front 9

Indefinite Integral Formula
∫ sinx dx =

Back 9

-cosx + C

Front 10

Indefinite Integral Formula
∫ cosx dx =

Back 10

sinx + C

Front 11

Indefinite Integral Formula
∫ sec^2 x dx =

Back 11

tanx + C

Front 12

Indefinite Integral Formula
∫ csc^2 x dx =

Back 12

-cotx + C

Front 13

Indefinite Integral Formula
∫ secx tanx dx =

Back 13

secx + C

Front 14

Indefinite Integral Formula
∫ cscx cotx dx =

Back 14

-cscx + C