Find indefinite integrals of hyperbolic functions

Error

There was an error loading the page.

Contributors

Feedback

From users who are not members of Content created by Newcastle University :

Bill Foster	said	Ready to use	6 years, 6 months ago
Gabriele De Chiara	said	Has some problems	9 years ago

History

○

Bill Foster 6 years, 6 months ago

Gave some feedback: Ready to use

○

Gabriele De Chiara commented 9 years ago

Hi, I understand that the constant C should be inserted, however if F(x) is a primitive of f(x), both F(x)+C and F(x)+1+C are two possible solutions. I am looking for a way to test the F'(x)=f(x) or that the difference of the student's solution from mine is constant.

○

Gabriele De Chiara 9 years ago

Gave some feedback: Has some problems

○

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Created this.

There is only one version of this question that you have access to.

There are 3 other versions that do you not have access to.

Question statement

Integrate the following functions $f(x)$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	9
b	integer	7
s2	integer	-1
s1	integer	1
a1	integer	7
b1	integer	-6

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..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
"Part a)" - prompt
"Part a)" → "Unnamed gap" - Correct answer

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

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

$f(x)=\simplify[std]{ cosh({a}x+{b})}$

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

You must include the constant of integration as $C$ .

Input all numbers as integers or fractions – not as decimals.

Advice

a) Since $\int \cosh(x)=\sinh(x)+C$ it follows that:

$\int \simplify[std]{cosh({a}x+{b})}\;dx = \frac{1}{\var{a}}\simplify[std]{ sinh({a}x+{b})}+C$

b) We perform integration by parts:

Using $\int u dv = uv - \int v du$ where:

$\begin{eqnarray*} &u&=x \Rightarrow du = dx \\ &dv& = \simplify[std]{sinh({a1}x+{b1})} \Rightarrow v= \simplify[std]{((cosh({a1}x+{b1}))/{a1})}\end{eqnarray*}$

Hence we have:

$\begin{eqnarray*} \int \simplify[std]{x*sinh({a1}x+{b1})}\;dx&=&\frac{1}{\var{a1}}\simplify[std]{x*cosh({a1}x+{b1})}-\frac{1}{\var{a1}} \int \simplify[std]{cosh({a1}x+{b1})}\;dx\\ &=&\frac{1}{\var{a1}}\simplify[std]{x*cosh({a1}x+{b1})}-\frac{1}{\var{a1^2}}\simplify[std]{sinh({a1}x+{b1})}+C \end{eqnarray*}$

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
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet

This question is used in the following exams:

Integration by parts by Newcastle University Mathematics and Statistics in Content created by Newcastle University.
Integration by parts by Henrik Skov Midtiby in SDS.
Luis's copy of Integration by parts by Luis Hernandez in MAT333.
Ann's copy of Integration by parts by Ann Smith in Calculus.
Integration by parts by Ann Smith in Calculus.
Integration by parts -section 8E by Kuldeep Singh in Kuldeep's workspace.
claire's copy of Integration by parts -section 8E by claire lines in claire's workspace.
Calculus by Morgiane Richard in Mathematics for Geosciences.

Loading...

Error

Find indefinite integrals of hyperbolic functions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bill Foster 6 years, 6 months ago

Gabriele De Chiara commented 9 years ago

Gabriele De Chiara 9 years ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Find indefinite integrals of hyperbolic functions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bill Foster 6 years, 6 months ago

Gabriele De Chiara commented 9 years ago

Gabriele De Chiara 9 years ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`