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Definite Integrals
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What does definite integration yield, unlike indefinite integration?

A specific numerical value

What are the two small numbers in ∫abf(x) dx\int_a^b f(x) \, dx called?

Limits

What does ∫abf(x) dx\int_a^b f(x) \, dx represent geometrically?

Net area under curve

If f(x)f(x) is positive over [a,b][a,b], what does ∫abf(x) dx\int_a^b f(x) \, dx represent?

Area between curve and x-axis

How do you find total area when f(x)f(x) has positive and negative values?

Integrate absolute value of f(x)f(x)

What is the Fundamental Theorem of Calculus formula?

F(b)−F(a)F(b) - F(a)

What happens to the constant CC in definite integrals?

It cancels out

What is ∫aaf(x) dx\int_a^a f(x) \, dx equal to?

0

What is the relationship between ∫abf(x) dx\int_a^b f(x) \, dx and ∫baf(x) dx\int_b^a f(x) \, dx?

They are negatives of each other

What is ∫abc⋅f(x) dx\int_a^b c \cdot f(x) \, dx equal to, where cc is constant?

c⋅∫abf(x) dxc \cdot \int_a^b f(x) \, dx

What does the additivity property state?

∫abf(x) dx+∫bcf(x) dx=∫acf(x) dx\int_a^b f(x) \, dx + \int_b^c f(x) \, dx = \int_a^c f(x) \, dx

Which is NOT mentioned as an application of definite integrals?

Population growth rates

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