Hina's copy of Julie's Integration 4

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Hina Ahmed

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Hina Ahmed 8 years, 4 months ago

Created this as a copy of Julie's 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	6
ans1	number	31.208
ans2	number	8.884
t	integer	1
tol	number	0.001
ans	number	31.208
b1	integer	3

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Value

xxxxxxxxxx
 
random(3..7 except 0)

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Description

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Generated value: `integer`

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Parts

Match choices with answers

Match choices with answers

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

Enter the area $A$ here to 3 decimal places:

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(no maximum)

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(no maximum)

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Answer 1
Answer 2

5

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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.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Hina Ahmed 8 years, 4 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

Match choices with answers

Advanced settings

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Hina's copy of Julie's Integration 4

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Hina Ahmed 8 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Match choices with answers

Advanced settings

Generated value: `integer`