Indefinite integral

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Bill Foster

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Bill Foster 55 years, 3 months ago

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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
Indefinite integral (custom feedback)	draft	Clodagh Carroll	26/03/2019 18:00

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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	3
b	integer	8
s3	integer	1
s2	integer	1
s1	integer	1
s5	integer	1
s4	integer	1
a1	integer	4
a2	integer	3
b1	integer	5
c3	integer	7

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s1*random(2..5)

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Generated value: `integer`

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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 $C$ .

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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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Bill Foster 55 years, 3 months ago

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Generated value: `integer`

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Indefinite integral

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 55 years, 3 months ago

Error in variable testing condition

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Warning

Generated value: integer

Parts

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Generated value: `integer`