Simon's copy of Julie's copy of Indefinite integral

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Simon Thomas 6 years, 1 month ago

Created this as a copy of Julie's copy of Indefinite integral.

Name	Status	Author	Last Modified
Indefinite integral	draft	Bill Foster	06/08/2020 08:41
Julie's copy of Indefinite integral	draft	Julie Crowley	06/02/2017 15:33
Simon's copy of Julie's copy of Indefinite integral	draft	Simon Thomas	21/03/2019 10:24
Indefinite integral 2 (custom feedback)	draft	Clodagh Carroll	09/03/2020 11:10
Jo-Ann's Indefinite integrals	draft	Jo-Ann Lyons	17/04/2019 13:24
Jo-Ann's copy of Indefinite integral	draft	Jo-Ann Lyons	17/04/2019 14:15
Indefinite integral 2	Ready to use	Jo-Ann Lyons	24/04/2019 15:29
Indefinite integral 2	Ready to use	Jo-Ann Lyons	24/04/2019 15:31
Indefinite integral 2	draft	Xiaodan Leng	10/07/2019 21:57
Indefinite integral 2	draft	Xiaodan Leng	10/07/2019 21:58

There are 8 other versions that do you not have access to.

Question statement

Find the following indefinite integral.

Input the constant of integration as $C$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

b	integer	3
n	integer	4
a	integer	6
d	integer	5

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Value

xxxxxxxxxx
 
random(2..5)

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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

Gap-fill
1. Gap Mathematical expression
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Gap-fill

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

$\displaystyle \int \simplify[std]{{b}/(({a}*x+{d})^{n})} dx= \phantom{{}}$ Unnamed gap

Input all numbers as integers or fractions and not decimals. Remember to include the constant of integration $C$ .

Advice

Let $u = \simplify[std]{{a}*x+{d}}$ . Then,

$\simplify[std]{{b}/(({a}*x+{d})^{n})} = \simplify[std]{{b}/(u^{n})}.$

Now,

$\int \simplify[std]{{b}/({a}*x+{d})^{n}} dx = \int \simplify[std]{{b}/(u^{n})} \frac{dx}{du} du.$

Rearrange $u = \simplify[std]{{a}x+{d}}$ to get $\displaystyle x = \simplify[std]{(u-{b})/{a}}$ , and hence $\displaystyle\frac{dx}{du} = \frac{1}{\var{a}}$ .

$\displaystyle \int \frac{1}{u^n} du = -\frac{1}{(n-1)u^{n-1}} + C$ is a standard integral, so we can now calculate the desired integral:

$\int \simplify[std]{{b}/(u^{n})} \frac{dx}{du} du = \simplify[std]{{b}/({n-1}*u^{n-1})} \cdot \frac{1}{\var{a}} + C = \simplify[std]{(-{b})/({a*(n-1)}*({a}*x+{d})^{n-1}) + C}.$

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Simon's copy of Julie's copy of Indefinite integral

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Taxonomy: mathcentre

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Simon Thomas 6 years, 1 month ago

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Simon's copy of Julie's copy of Indefinite integral

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`