Luis's copy of Integration: Indefinite integral

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Luis Hernandez 6 years, 4 months ago

Created this as a copy of Integration: Indefinite integral.

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

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Question statement

Integrate the following function $f(x)$ .

Input the constant of integration as $C$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	-4
b	integer	-2
s3	integer	1
s2	integer	-1
s1	integer	-1
s5	integer	1
s4	integer	-1
a1	integer	3
a2	integer	-5
b1	integer	7
c3	integer	5

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
s1*random(2..5)

JME function reference

Description

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

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Generated value: `integer`

-4

← Depends on:

→ Used by:

Advice
"Unnamed part" - prompt
"Unnamed part" → "Unnamed gap" - Correct answer

Parts

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1. Gap Mathematical expression
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1. Step Information only

Gap-fill

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$\simplify[std]{f(x) = {b} * e ^ ({a}*x) + {b1} * Sin({a1}*x) + {a2} * x ^ {c3}}$

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

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

Click on Show steps to get more information. You will not lose any marks by doing so.

Advice

Note that

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

Splitting the integral into three parts and using the above information we have:

$\begin{eqnarray*}\simplify[std]{Int({b} * e ^ ({a}*x) + {b1} * Sin({a1}*x) + {a2} * x ^ {c3},x)}&=&\simplify[std]{Int({b} * e ^ ({a}*x),x)+Int({b1} * Sin({a1}*x),x)+Int({a2} * x ^ {c3},x) }\\ &=&\simplify[std]{({b}/{a}) * (e ^({a}*x)) + (({(-b1)}/{a1}) * Cos({a1}*x)) + ({a2}/{c3+1}) * (x ^ {(c3 + 1)})+C} \end{eqnarray*}$

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Luis's copy of Integration: Indefinite integral

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Taxonomy: mathcentre

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Luis Hernandez 6 years, 4 months ago

Error in variable testing condition

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Generated value: `integer`

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Error

Luis's copy of Integration: Indefinite integral

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Luis Hernandez 6 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`