Applications of Integration (HSC SSCE Mathematics Advanced): Quizzes

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Applications of Integration
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How are areas below the xx-axis represented when calculating definite integrals?

As negative numbers

What is the key principle for finding total area when a curve crosses the xx-axis?

Evaluate separate integrals, then combine

For area between curves where f(x)f(x) is above g(x)g(x), which formula is correct?

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

What is the period of y=cos⁡12xy = \cos\frac{1}{2}x?

4π4\pi

For y=cos⁡12xy = \cos\frac{1}{2}x on [0,4π][0, 4\pi], what is the total area between curve and xx-axis?

8 square units

When finding area between two curves, which function should you subtract?

Subtract the lower from the upper

What is the area between y=sin⁡xy = \sin x and y=sin⁡2xy = \sin 2x on [0,π3][0, \frac{\pi}{3}]?

14\frac{1}{4} square units

Where do y=sin⁡xy = \sin x and y=cos⁡xy = \cos x intersect in [0,2π][0, 2\pi]?

x=π4x = \frac{\pi}{4} and x=5π4x = \frac{5\pi}{4}

When calculating total area, how should negative integrals be treated?

Take the absolute value

What should always be done before attempting to integrate for areas?

Sketch the curve

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