Antidifferentiation of Polynomial Functions (VCE SSCE Mathematical Methods): Flashcards

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Antidifferentiation of Polynomial Functions
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Antidifferentiation definition

Reverse process of differentiation

Constant of integration symbol

cc

Power rule: xndx\int x^n \, dx

xn+1n+1+c\frac{x^{n+1}}{n+1} + c

Power rule process

Increase power by 1, divide by new power

Functions w/ same derivative differ by

A constant

Constant multiple rule formula

kf(x)dx=kf(x)dx\int k f(x) dx = k \int f(x) dx

How to antidifferentiate polynomials

Term by term

Find specific antiderivative using

Boundary condition to find cc

Constants needed for polynomial antiderivative

One cc at the end

1dx\int 1 \, dx

x+cx + c

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