Indefinite integral

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Bill Foster

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Bill Foster 55 years, 4 months ago

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Name	Status	Author	Last Modified
Indefinite integral	draft	Bill Foster	06/08/2020 08:41
Question 2	draft	TEAME UCC	07/10/2016 22:50
INT3	draft	Gagan Aggarwal	04/05/2021 13:31

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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	2
c	integer	9
b	integer	5
d	integer	2
s1	integer	1
m	integer	9
n	integer	11
r	integer	1

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$\simplify[std]{f(x) = {c}x ^ {m} + {d}*x^({b}/{n})}$

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

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

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Using

$\int \;x^n\;dx=\frac{x^{n+1}}{n+1}+C$ for any number

$n \neq -1$ we have

$\begin{eqnarray*} \simplify[std]{Int({c}*x^{m}+{d}*x ^ ({b} / {n}),x)} &=&\simplify[std]{ ({c} / {m + 1}) * x ^ {m + 1} +{d}* x ^ ({b} / {n} + 1) / ({b} / {n} + 1) + C }\\ &=&\simplify[std]{ ({c} / {m + 1}) * x ^ {m + 1} + ({d*n} / {b + n}) * x ^ ({b + n} / {n}) + C} \end{eqnarray*}$

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Taxonomy: mathcentre

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Bill Foster 55 years, 4 months ago

Error in variable testing condition

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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, 4 months ago

Error in variable testing condition

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Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`