Ch1: Integration by parts

Error

There was an error loading the page.

Contributors

Graham Wynn

Feedback

From users who are not members of Graham's workspace :

Christian Lawson-Perfect

said

Ready to use

8 years, 10 months ago

History

○

Christian Lawson-Perfect 8 years, 10 months ago

Gave some feedback: Ready to use

○

Graham Wynn 9 years, 6 months ago

Created this as a copy of Integration by parts - Ch 1.

Name	Status	Author	Last Modified
Integration by parts	Ready to use	Bill Foster	01/06/2016 09:47
Katie's copy of Integration by parts	Ready to use	Katie Dexter	01/06/2016 09:47
Integration by parts 1	Ready to use	joshua boddy	01/06/2016 09:47
Integration by parts 1 with limits	Ready to use	joshua boddy	01/06/2016 09:47
Integration by parts - Ch 1	Ready to use	Katie Dexter	01/06/2016 09:47
Ch1: Integration by parts	Ready to use	Graham Wynn	01/06/2016 09:47

There are 2 other versions that do you not have access to.

Question statement

Find the following indefinite integral.

Give any introductory information the student needs.

			Name	Type	Generated Value

s3	integer	-1
c	integer	-2
b	integer	3
m	integer	4

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:

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.

$I=\displaystyle \int \simplify[std]{x*({b}x+{c})^{m}} dx$

Leave your answer in the form of $\frac{(ax+b)^d}{e}*g(x) + C$ with your constant of integration as "+ C".

$I=\;$ Unnamed gap

You can get help by clicking on show steps.

Advice

The formula for integrating by parts is

$\int u\frac{dv}{dx} dx = uv - \int v \frac{du}{dx} dx.$

We choose $u = x$ and $\displaystyle \frac{dv}{dx} = \simplify[std]{({b}*x+{c})^{m}}$ .

So $\displaystyle \frac{du}{dx}$ = $1$ and $\displaystyle v = \simplify[std]{(1/{(m+1)*b})*({b}*x+{c})^{m+1}}$ .

Hence,

$\begin{eqnarray*} \displaystyle \int \simplify[std]{x*({b}x+{c})^{m}} dx &=& uv - \int v \frac{du}{dx} dx \\ &=& \simplify[std]{(x/{(m+1)*b})*({b}*x+{c})^{m+1} - (1/{(m+1)*b})*Int (({b}*x+{c})^{m+1}, x)} \\ &=& \simplify[std]{(x/{(m+1)*b})*({b}*x+{c})^{m+1} - (1/{(m+1)*(m+2)*b^2})*({b}*x+{c})^{m+2}+C} \\ &=&\simplify[std]{({b}*x+{c})^{m+1}/{(m+1)*(m+2)*b^2}*({b*(m+2)}x - ({b}x+{c}))+C}\\ &=&\simplify[std]{({b}*x+{c})^{m+1}/{(m+1)*(m+2)*b^2}*({b*(m+1)}x - {c})+C} \end{eqnarray*}$
The solution is:

$\simplify[std]{g(x)={b*(m+1)}*x-{c}}$ .

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

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 8 years, 10 months ago

Graham Wynn 9 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Ch1: Integration by parts

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 8 years, 10 months ago

Graham Wynn 9 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`