Luis's copy of Indefinite integral by substitution

Error

There was an error loading the page.

Contributors

History

○

Luis Hernandez 6 years, 3 months ago

Created this as a copy of Indefinite integral by substitution.

Name	Status	Author	Last Modified
Indefinite integral by substitution	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Luis's copy of Indefinite integral by substitution	draft	Luis Hernandez	30/11/2018 18:36

There are 6 other versions that do you not have access to.

Question statement

Find the following integral.

Input the constant of integration as $C$ .

Input all numbers as integers or fractions not as decimals.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	6
s1	integer	1
b	integer	5
m	integer	8

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..9)

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`

→ Used by:

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

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.

$I=\simplify[std]{Int( sin(x)*({a} + {b}*cos(x))^{m},x)}$

Input all numbers as integers or fractions.

$I=\;$ Unnamed gap

Input the constant of integration as $C$ .

Click on Show steps if you need help. You will lose 1 mark if you do so.

Advice

This exercise is best solved by using substitution.
Note that if we let $u=\simplify[std]{{a}+{b}cos(x)}$ then $du=\simplify[std]{({-b}*sin(x))*dx }$
Hence we can replace $\sin(x)\;dx$ by $\frac{1}{\var{-b}}\;du$ .

Hence the integral becomes:

$\begin{eqnarray*} I&=&\simplify[std]{Int((1/{-b})u^{m},u)}\\ &=&\simplify[std]{(1/{-b})u^{m+1}/{m+1}+C}\\ &=& \simplify[std]{({a}+{b}*cos(x))^{m+1}/{-b*(m+1)}+C} \end{eqnarray*}$

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 not used in any exams.

Loading...

Error

Luis's copy of Indefinite integral by substitution

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Luis Hernandez 6 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Luis's copy of Indefinite integral by substitution

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Luis Hernandez 6 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`