Julie's Integration 4

Error

There was an error loading the page.

Contributors

Julie Crowley

History

○

Julie Crowley 8 years, 7 months ago

Published this.

○

Julie Crowley 10 years, 5 months ago

Created this as a copy of Leicester: Integration 4.

Name	Status	Author	Last Modified
Julie's Integration 4	draft	Julie Crowley	08/10/2016 21:59
Integration 4	draft	Christian Lawson-Perfect	06/08/2020 08:41
Hina's copy of Julie's Integration 4	draft	Hina Ahmed	08/11/2016 18:05

There are 10 other versions that do you not have access to.

Question statement

Find the area $A$ of the shape bounded by the $x$ -axis, the function $y=\simplify[std]{{t}*exp({b}/{c}*x)+{1-t}*ln({b}x+{c})}$ and the lines $x=\var{b1},\;x=\var{b2}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

c	integer	6
b	integer	3
b2	integer	4
ans1	number	9.342
ans2	number	5.403
t	integer	0
tol	number	0.001
ans	number	5.403
b1	integer	2

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(3..7 except 0)

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: `integer`

This variable doesn't seem to be used anywhere.

Advice

First we observe that:

$\simplify[std]{int ({t}*exp({b}/{c}*x)+{1-t}*ln({b}x+{c}),x)={t*c}/{b}*exp({b}/{c}*x)+({1-t}/{b}*({b}x+{c})*(ln({b}x+{c})-1))+C}.$

Hence we have:

$\begin{eqnarray*} \simplify[std]{defint ({t}*exp({b}/{c}*x)+{1-t}*ln({b}x+{c}),x,{b1},{b2})}&=&\left[\simplify[std]{{t*c}/{b}*exp({b}/{c}*x)+({1-t}/{b}*({b}x+{c})*(ln({b}x+{c})-1))}\right]_{\var{b1}}^{\var{b2}}\\&=&\var{ans}\end{eqnarray*}$

to 3 decimal places.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

All of Integration by Julie Crowley in Julie's workspace.
Methods of Integration by Deirdre Casey in Deirdre's workspace.
My Test Exam by Kieran Mulchrone in Kieran's workspace.
Methods of integration by Simon Thomas in Maths support.
Markus's copy of Methods of Integration by Markus Schmied in Markus's workspace.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Julie Crowley 8 years, 7 months ago

Julie Crowley 10 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Number entry

Advanced settings

Loading...

Error

Julie's Integration 4

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Julie Crowley 8 years, 7 months ago

Julie Crowley 10 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Number entry

Advanced settings

Generated value: `integer`