Indefinite integral (custom feedback)

Error

There was an error loading the page.

Contributors

History

○

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

There are 11 other versions that do you not have access to.

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

s3	integer	-1
a	integer	5
a2	integer	6
b1	integer	-3
s2	integer	-1
s4	integer	1
c3	integer	3
s1	integer	1
a1	integer	5
s5	integer	1
b	integer	-5

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1,-1)

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `integer`

-1

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Mathematical expression
  Add
1. Step Information only

Gap-fill

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

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

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

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

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Information only

This question is used in the following exams:

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Clodagh Carroll 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Indefinite integral (custom feedback)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Clodagh Carroll 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`