Hyperbolic Functions 3

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Bill Foster

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Bill Foster 55 years, 2 months ago

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Question statement

Integrate the following functions $f(x)$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	6
b	integer	4
s2	integer	1
s1	integer	1
a1	integer	9
b1	integer	4

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..9)

JME function reference

Description

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

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Generated value: `integer`

This variable doesn't seem to be used anywhere.

Parts

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

Gap-fill

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

$f(x)=\simplify[std]{ cosh({a}x+{b})}$

$\displaystyle{\int f(x)\;dx=\;\;}$ Unnamed gap

You must include the constant of integration as $C$ .

Input all numbers as integers or fractions – not as decimals.

Advice

a)

$\int \simplify[std]{cosh({a}x+{b})}\;dx = \frac{1}{\var{a}}\simplify[std]{ sinh({a}x+{b})}+C$

b)

Integrate by parts, so that

$\begin{eqnarray*} \int \simplify[std]{x*sinh({a1}x+{b1})}\;dx&=&\int \simplify[std]{x*d((cosh({a1}x+{b1}))/{a1})}\\ &=&\frac{1}{\var{a1}}\simplify[std]{x*cosh({a1}x+{b1})}-\frac{1}{\var{a1}} \int \simplify[std]{cosh({a1}x+{b1})}\;dx\\ &=&\frac{1}{\var{a1}}\simplify[std]{x*cosh({a1}x+{b1})}-\frac{1}{\var{a1^2}}\simplify[std]{sinh({a1}x+{b1})}+C \end{eqnarray*}$

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This question is used in the following exams:

Symbology 101 by martin reed in martin's workspace.
Hyperbolic functions 1 by Bill Foster in Bill's workspace.
Maths Support: Hyperbolic functions by Christian Lawson-Perfect in Maths Support Wiki.
mathcentre: Hyperbolic functions by Newcastle University Mathematics and Statistics in mathcentre.
Second Examination by Kuldeep Singh in Kuldeep's workspace.
Calculous: 1 by Aneela Arshad in Aneela's workspace.
Integration by Bill Foster in Bill's workspace.
Michael's copy of mathcentre: Hyperbolic functions by Michael Proudman in .Algebra.
Questions on integration by Kuldeep Singh in Kuldeep's workspace.
Questions on integration - chapter 8 by Kuldeep Singh in Kuldeep's workspace.
mathcentre: Hyperbolic functions by Michael Proudman in Mathcentre based Materials.

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Checkpoint description

Bill Foster 55 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

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Hyperbolic Functions 3

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 55 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

Generated value: `integer`