Jo-Ann's copy of Integration by parts - logarithm

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Jo-Ann Lyons 5 years, 11 months ago

Created this as a copy of Integration by parts 4 - logarithm.

Name	Status	Author	Last Modified
Integration by parts	Ready to use	Bill Foster	01/06/2016 09:47
Integration by parts 2 - cos and sin	Ready to use	joshua boddy	01/06/2016 09:47
Integration by parts 3 - exponential	Ready to use	joshua boddy	01/06/2016 09:47
Integration by parts 4 - logarithm	Ready to use	joshua boddy	01/06/2016 09:47
Integration by parts 2 - cos and sin with limits	Ready to use	joshua boddy	01/06/2016 09:47
Integration by parts 3 - exponential with limits	Ready to use	joshua boddy	01/06/2016 09:47
Integration by parts 4 - logarithm with limits	Ready to use	joshua boddy	01/06/2016 09:47
Integration by parts 2 - cos and sin with limits 19/10	Ready to use	Katie Dexter	01/06/2016 09:47
Jo-Ann's copy of Integration by parts - logarithm	draft	Jo-Ann Lyons	25/04/2019 12:33
Maria's copy of Jo-Ann's copy of Integration by parts - logarithm	draft	Maria Aneiros	27/05/2019 07:24
Integration by parts 2 - cos and sin	draft	Xiaodan Leng	11/07/2019 06:46

There are 32 other versions that do you not have access to.

Question statement

Find the following indefinite integral.

This question is scaffolded - i.e. it takes you through answering the question step by step.

Input all numbers as fractions or integers and not decimals.

Don't forget $C$ !

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	3
c	integer	3
b	integer	-7
d	integer	4
s2	integer	1
s1	integer	-1

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..5)

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Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

Advice
"Part a)" - prompt
"Part a)" → "Gap 1." - Correct answer
"Part b)" → "Gap 1." - Correct answer
"Part c)" → "Gap 0." - Correct answer
"Part c)" → "Gap 1." - Correct answer
"Part d)" - prompt
"Part d)" → "Unnamed gap" - Correct answer

Parts

Part a) Gap-fill
1. Gap Gap 0. Mathematical expression
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2. Gap Gap 1. Mathematical expression
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Part b) Gap-fill
1. Gap Gap 0. Mathematical expression
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2. Gap Gap 1. Mathematical expression
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Part c) Gap-fill
1. Gap Gap 0. Mathematical expression
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2. Gap Gap 1. Mathematical expression
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Part d) Gap-fill
1. Gap Mathematical expression
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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$I=\displaystyle \int \simplify[std]{({a}x)*ln({c}x)} dx$

The formula for integration by parts is

$\int u\frac{dv}{dx} dx = uv - \int v \frac{du}{dx} dx.$

What is the most suitable choice for $u$ and $\frac{dv}{dx}$ ?

$u =\;$ Gap 0.

$\frac{dv}{dx} =\;$ Gap 1.

Advice

The formula for integrating by parts is

$\int u\frac{dv}{dx} dx = uv - \int v \frac{du}{dx} dx.$

We choose $u = \simplify[std]{ln{c}x}$ and $\displaystyle \frac{dv}{dx} = \simplify[std]{{a}x}$ .

So $\displaystyle \frac{du}{dx} = \simplify[std]{1/x}$ and $\displaystyle v = \simplify[std]{({a}x^2/2)}$ .

Hence,

$\begin{eqnarray} \int \simplify[std]{({a}*x)*ln({c}*x)} dx &=& uv - \int v \frac{du}{dx} dx \\ &=& \simplify[std]{(({a}*x^2)/2)*ln({c}*x) - Int(({a}*x/2),x)} \\ &=& \simplify[std]{(({a}x^2)/2)*ln({c}*x) -({a}x^2/4) + C} \end{eqnarray}$

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Jo-Ann's copy of Integration by parts - logarithm

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

Jo-Ann Lyons 5 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

The formula for integrating by parts is

Loading...

Error

Jo-Ann's copy of Integration by parts - logarithm

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Jo-Ann Lyons 5 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

The formula for integrating by parts is

Generated value: `integer`