Integration 3 - Substitution - Numbas at mathcentre.ac.uk

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Xiaodan Leng 5 years, 9 months ago

Created this as a copy of Integration 3 - Substitution.

Name	Status	Author	Last Modified
Integration 2 - Substitution	Ready to use	Katie Lester	01/06/2016 09:47
Integration 3 - Substitution	Ready to use	Katie Lester	01/06/2016 09:47
Integration 2 - Substitution 15/10	Ready to use	Katie Dexter	01/06/2016 09:47
Integration 2 - Substitution	draft	Xiaodan Leng	11/07/2019 06:48
Integration 3 - Substitution	draft	Xiaodan Leng	11/07/2019 06:49

There are 12 other versions that do you not have access to.

Question statement

Integrate the following by substitution.

You may assume the constant of integration is zero for the purposes of these questions.

Give any introductory information the student needs.

			Name	Type	Generated Value

			c	list	List of 9 items
			p	list	[ 5, 2, 3, 5, 5 ]

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(-5..5 except 0 except 1 except -1),9)

JME function reference

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: `list`

[ 4, -2, 3, -5, -3, 2, 4, -4, 3 ]

Parts

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

Gap-fill

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

Use $u=\simplify{{c[1]}x+{c[2]}}$ as your substitution.

$\simplify{Int({c[0]}x*({c[1]}x+{c[2]})^{p[0]},x)}$

$=\int$ Gap 1. $du$

$=$ Gap 0.

Advice

If you do not understand how to begin these questions, please see 'Integration 1 - Substitution'.

The difference with these questions is that you must rearrange the $u=$ equation for $x$ and put this in after the $dx$ substitution as it does not nicely cancel as it did before.

Once you have done this, it should be clear that you then multiply through the brackets and integrate the two remaining terms with respect to $u$ .

Remember to replace the ' $u$ 's at the end.

Give a worked solution to the whole question.

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet

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Integration 3 - Substitution

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

Xiaodan Leng 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

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Error

Integration 3 - Substitution

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`