Musa's copy of 3 Integration: solving for constant

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Musa Mammadov 1 year, 10 months ago

Published this.

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Kerri Morgan was given access to the Musa's copy of 3 Integration: solving for constant 2 years, 8 months ago

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Julien Ugon was given access to the Musa's copy of 3 Integration: solving for constant 2 years, 8 months ago

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Musa Mammadov 4 years, 11 months ago

Created this as a copy of Musa's copy of Integration: solving for constant.

Name	Status	Author	Last Modified
Integration: Indefinite integral	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Luis's copy of Integration: Indefinite integral	draft	Luis Hernandez	30/11/2018 18:29
Musa's copy of 3 Integration: Indefinite integral	draft	Musa Mammadov	27/06/2023 01:39
Musa's copy of 3 Integration: solving for constant	draft	Musa Mammadov	27/06/2023 01:39

There are 7 other versions that do you not have access to.

Question statement

Find the orginal function $f(x)$ given $f^\prime (x)$ and value $f(x_0) = C_0;$ that is solve for constant for $\int f^\prime (x) \,dx.$

Give any introductory information the student needs.

			Name	Type	Generated Value

a5	integer	4
an5	integer	6
c5	integer	-3
x0	integer	2
C0	integer	2
a52	integer	5
an52	integer	6
c52	integer	-2
x02	integer	2
C02	integer	7
a	integer	-4
an	integer	1
c	integer	-9
xp0	integer	2
Cp0	integer	2
xp02	integer	2
Cp02	integer	3
c2	integer	-8
an2	integer	-1
a2	integer	4

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-5..5 except [-1,0,1])

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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`

→ Used by:

"Part a)" - prompt
"Part a)" → "Gap 0." - Correct answer
"Part a)" → "Gap 1." - Correct answer

Parts

Part a) Gap-fill
1. Gap Gap 0. Mathematical expression
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2. Gap Gap 1. Mathematical expression
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1. Step Information only
Part b) Gap-fill
1. Gap Gap 0. Mathematical expression
  Add
2. Gap Gap 1. Mathematical expression
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1. Step Information only

Gap-fill

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

$f^\prime (x) = \simplify[std]{ {a5}* x^{an5}+ {c5}}, ~~~ f(\var{x0}) = \var{C0}$

$\displaystyle \int\;(\simplify[std]{ {a5}* x^{an5}+ {c5}})\,dx=\;$ Gap 0.

$f (x)=\;$ Gap 1.

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

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Advice

Note that

$\begin{eqnarray*} &\int& \;x^n\;dx&=&\frac{x^{n+1}}{n+1}+C,\;\;n \neq -1\\ &\int& \;\sin(ax)\;dx &=& -\frac{1}{a}\cos(ax)+C\\ &\int& \;e^{ax}\;dx &=& \frac{1}{a}e^{ax}+C\\ \end{eqnarray*}$

First integrate:

(*) $\int f^\prime (x)\,dx$ = $\int\;(a x^n+ c)\,dx=\; \frac{a}{n+1}x^{n+1} + cx +C$

then calculate the value of $C$ from

$\frac{a}{n+1}x_0^{n+1} + cx_0 +C = C_0$

and put in back to (*).

Give a worked solution to the whole question.

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Musa's copy of 3 Integration: solving for constant

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

Musa Mammadov 1 year, 10 months ago

Kerri Morgan was given access to the Musa's copy of 3 Integration: solving for constant 2 years, 8 months ago

Julien Ugon was given access to the Musa's copy of 3 Integration: solving for constant 2 years, 8 months ago

Musa Mammadov 4 years, 11 months ago

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Musa's copy of 3 Integration: solving for constant

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Musa Mammadov 1 year, 10 months ago

Kerri Morgan was given access to the Musa's copy of 3 Integration: solving for constant 2 years, 8 months ago

Julien Ugon was given access to the Musa's copy of 3 Integration: solving for constant 2 years, 8 months ago

Musa Mammadov 4 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`