Quick questions on Areas between curves and volumes of revolution using definite integrals

3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are area between two curves?

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f(x) \geq g(x)

[a, b]

, the area between them is

What is volume of revolution about the

x

-axis?

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Rotating the region under

y = f(x)

between

x = a

and

x = b

about the

x

-axis produces a solid whose cross sections perpendicular to the axis are disks of radius

f(x)

. The volume is

What is volume of revolution about the

y

-axis?

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Rotating the region between

x = h(y)

and the

y

-axis, between

y = c

and

y = d

, about the

y

-axis gives

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