Applications of Integration (HSC SSCE Mathematics Advanced): Quizzes

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Applications of Integration
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Why must you sketch the region before calculating an area using integration?

To identify if area is below x-axis

What happens when a definite integral calculates an area below the x-axis?

The integral gives a negative value

If ∫abf(x)dx=−5\int_a^b f(x) dx = -5 for a region below the x-axis, what is the actual area?

5 square units

What is the formula for area between curves where f(x)f(x) is above g(x)g(x) on [a,b][a,b]?

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

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

Subtract lower from upper

What is ∫exdx\int e^x dx equal to?

ex+Ce^x + C

For y=ex−ey = e^x - e, what is the x-intercept?

x=1x = 1

If y=exy = e^x is shifted down by ee units, what is the new horizontal asymptote?

y=−ey = -e

What is the area between y=ex−ey = e^x - e, the x-axis, and y-axis (from x=0x=0 to x=1x=1)?

1 square unit

Before setting up an integral for area between curves, what must you identify?

Which curve is on top

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