Applications of Integration (HSC SSCE Mathematics Advanced): Flashcards

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Applications of Integration
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Areas below x-axis in definite integrals

Represented as negative numbers

Key principle for regions above/below x-axis

Evaluate separate integrals, then combine

Formula: area between curves where f(x)geqg(x)f(x) geq g(x)

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

Which function to subtract for area between curves

Subtract lower function from upper function

How to find intersection points of two curves

Set the two functions equal to each other

What to use for negative integrals in total area

Absolute value

Why sketch curve before integrating

Identify regions above/below x-axis

Period of y=cos⁡12xy = \cos\frac{1}{2}x

4π4\pi

How to check which curve is on top in an interval

Test a value in the interval

Antiderivative of cos⁡12x\cos\frac{1}{2}x

2sin⁡12x+C2\sin\frac{1}{2}x + C

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