Recognise and apply a standard integral - subexpressions version

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Christian Lawson-Perfect 4 years, 6 months ago

Published this.

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Christian Lawson-Perfect 4 years, 7 months ago

Created this.

Name	Status	Author	Last Modified
Recognise and apply a standard integral - subexpressions version	draft	Christian Lawson-Perfect	04/05/2023 17:08
MOEILIJK: Integratie van gekozen functies	draft	Alexander Holvoet	02/06/2024 14:37

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Question statement

Let $f(x) = \simplify{{function}}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

functions	list	Nested 4×3 list
scenario	list	List of 3 items
k	integer	5
function	expression	x^5
integral	expression	(1/(5 + 1))*x^(5 + 1)
derivative	expression	5^x^(5 - 1)
raw_function	expression	x^k
raw_integral	expression	(1/(k + 1))*x^(k + 1)

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
[
  ["x^k", "1/(k+1)*x^(k+1)", "k^x^(k-1)"],
  ["e^(k*x)", "1/k * e^(k*x)", "k*e^(k*x)"],
  ["sin(k*x)", "-1/k * cos(k*x)", "k*cos(k*x)"],
  ["cos(k*x)", "1/k * sin(k*x)", "-k*sin(k*x)"]
]

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`

[ [ "x^k", "1/(k+1)*x^(k+1)", "k^x^(k-1)" ], [ "e^(k*x)", "1/k * e^(k*x)", "k*e^(k*x)" ], [ "sin(k*x)", "-1/k * cos(k*x)", "k*cos(k*x)" ], [ "cos(k*x)", "1/k * sin(k*x)", "-k*sin(k*x)" ] ]

→ Used by:

scenario

This variable doesn't seem to be used anywhere.

Advice

$f(x) = \simplify{ {function} }$ .

The integral of $\var{raw_function}$ with respect to $x$ is $\var{raw_integral}$ .

Here, $k = \var{k}$ , so

$\int f(x) \, \mathrm{d}x = \simplify{ {integral} }$

Give a worked solution to the whole question.

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Recognise and apply a standard integral - subexpressions version

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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History

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Christian Lawson-Perfect 4 years, 6 months ago

Christian Lawson-Perfect 4 years, 7 months ago

Error in variable testing condition

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Generated value: `list`

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Mathematical expression

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Recognise and apply a standard integral - subexpressions version

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Christian Lawson-Perfect 4 years, 6 months ago

Christian Lawson-Perfect 4 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `list`