Applications of Integration (HSC SSCE Mathematics Advanced): Flashcards

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Applications of Integration
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Why sketch region before calculating area via integration?

To check if below x-axis (negative) & identify top curve

Sign of definite integral for area below x-axis

Negative

What to do if integral result is negative?

Take absolute value to find actual area

Area between y=f(x)y=f(x) above y=g(x)y=g(x), aa to bb

∫ab(f(x)−g(x)) dx\int_a^b (f(x) - g(x)) \, dx

In area between curves, which function subtract?

Subtract lower from upper function

∫ex dx=?\int e^x \, dx = ?

ex+Ce^x + C

How to identify which curve is on top?

Draw a sketch

What should integration limits match?

Boundaries of the region

Horizontal asymptote of y=exy = e^x

y=0y = 0

∫e dx=?\int e \, dx = ? (where ee is constant)

ex+Cex + C

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