Rates and Integration (HSC SSCE Mathematics Advanced): Flashcards

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Rates and Integration
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Relationship between integration and differentiation

Inverse operations

Symbol for rate of change of QQ with respect to tt

dQdt\frac{dQ}{dt}

Always include this when integrating

Constant of integration (CC)

Used to find value of constant CC

Initial or boundary condition

When dQdt=0\frac{dQ}{dt} = 0, quantity QQ is

Stationary (neither increasing nor decreasing)

When rate is positive, quantity is

Increasing

When rate is negative, quantity is

Decreasing

eax+bdx=\int e^{ax+b} dx =

1aeax+b+C\frac{1}{a}e^{ax+b} + C

When integrating eax+be^{ax+b}, divide by

Coefficient of the variable (aa)

Sign of exe^x for all values of xx

Always positive

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