Unit 01 - Essential problems

Shells

01

Shells volume - offset graph, -axis

Consider the region in the first quadrant bounded by the lines , , , and the curve . Revolve this about the -axis.

Find the volume of the resulting solid.

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IBP

03

Integration by parts - A and T

Compute the integral:

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06

Integration by parts - A and L

Compute the integral:

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08

Integration by parts - A and I

Compute the integral:

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Trig power products

01

Somewhat odd power product

Compute the integral:

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02

Tangent and secant both even

Compute the integral:

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03

All even power product

Compute the integral:

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07

Tangent and secant mixed parity

Compute the integral:

• (a) Using .
• (b) Using .

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Trig subs

04

Trig sub

Compute the definite integral:

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09

Trig sub

Compute the integral:

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11

Trig sub

Compute the integral:

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Partial fractions

01

Distinct linear factors

Compute the integral:

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02

Long division first

Compute the integral:

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02

Long division first

Compute the integral:

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09

Partial fractions - repeated factor

Compute the integral:

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Simpson’s Rule

10

Simpson’s Rule for volume by shells

Use Simpson’s Rule with to compute the volume of the solid obtained by revolving the pictured region about the -axis. Can you do it without using a calculator?

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11

Area of a garden bed

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