The Exponential and Logarithmic Functions (HSC SSCE Mathematics Advanced): Flashcards

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Further Applications of Integration
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Primitive of 1x\frac{1}{x}

logex+C\log_e|x| + C

Formula for area between curves

ab\int_a^b (top curve - bottom curve) dxdx

In area formula, what are aa and bb?

xx-coordinates of intersection points

Which curve to subtract in area formula?

Subtract bottom curve from top curve

Value of loge1\log_e 1

00

Integral of kx\frac{k}{x}

klogex+Ck\log_e|x| + C

Asymptotes of rectangular hyperbola xy=2xy = 2

Both coordinate axes

Why use absolute value in logex\log_e|x|?

To ensure function defined for all non-zero values

First step in finding area between curves

Find intersection points

How to express final area answer?

Exact form (with logs) and decimal approximation

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