Integration (Negative and Fractional Powers) 2

Error

There was an error loading the page.

Contributors

Ben McGovern

Feedback

From users who are members of MASH Bath: Question Bank :

Ben McGovern

said

Has some problems

4 years ago

History

○

Christian Lawson-Perfect 2 years, 7 months ago

Published this.

○

Ben McGovern 4 years ago

Gave some feedback: Has some problems

○

Ben McGovern 4 years, 8 months ago

Created this as a copy of Integration: Using a Table of Integrals 2.

Name	Status	Author	Last Modified
Differentiation: Using a Table of Derivatives 2	Ready to use	Ben McGovern	26/09/2022 12:10
Differentiation: Using a Table of Derivatives 3	Ready to use	Ben McGovern	26/09/2022 12:11
Differentiation: Using a Table of Derivatives 4	Ready to use	Ben McGovern	26/09/2022 12:11
Differentiation: Using a Table of Derivatives 5a	Ready to use	Ben McGovern	26/09/2022 12:11
Differentiation: Using a Table of Derivatives 5b	Ready to use	Ben McGovern	26/09/2022 12:12
Differentiation: Using a Table of Derivatives 5c	Ready to use	Ben McGovern	26/09/2022 12:12
Differentiation (Harder powers - negative and fractions) 2	Ready to use	Ben McGovern	04/05/2023 05:42
Differentiation: Stationary Points and their Nature 1	Ready to use	Ben McGovern	26/09/2022 11:56
Differentiation: Stationary Points and their Nature 2	Ready to use	Ben McGovern	26/09/2022 11:56
Integration: Using a Table of Integrals 2	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 3a	Ready to use	Ben McGovern	13/02/2023 10:37
Integration: Using a Table of Integrals 3b	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 4	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 5a	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 5b	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 5c	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 6	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 1a i	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 1b	Ready to use	Ben McGovern	23/02/2023 12:45
Integration: By Substitution 1c	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 2a	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 2b	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 2c	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 3a i	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 3c	Ready to use	Ben McGovern	27/09/2022 09:01
Integration (Negative and Fractional Powers) 2	Has some problems	Ben McGovern	27/09/2022 09:01
Integration (Negative and Fractional Powers) 3	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Definite Integrals 2	Ready to use	Ben McGovern	26/09/2022 12:18
Integration: By Substitution 1a ii (Negative and Fractional Powers)	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 3a ii (Negative and Fractional Powers)	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Definite Integrals 3	Ready to use	Ben McGovern	26/09/2022 12:18
Integration: Definite Integrals 4	Ready to use	Ben McGovern	26/09/2022 12:19
CB2 Differentiating polynomials 2	Ready to use	Mash Sheffield	17/04/2025 09:02
CD3 Integration - Substitution	Ready to use	Andrew Neate	17/04/2025 09:02
CB4 Definite integration	Ready to use	Andrew Neate	17/04/2025 09:02
CB6 Differentiating Trig 1	Ready to use	Andrew Neate	17/04/2025 09:02
CB7 Differentiating Trig 2	Ready to use	Andrew Neate	17/04/2025 09:02
CB8 Differentiating with Trig 3	Ready to use	Andrew Neate	17/04/2025 09:02
CB9 Differentiating with Exponentials	Ready to use	Andrew Neate	17/04/2025 09:02
CB10 Differentiation with logs	Ready to use	Andrew Neate	17/04/2025 09:02
CB3 - Indefinite integration - polynomials	Ready to use	Andrew Neate	17/04/2025 09:02
CB5 - Finding turning points	Ready to use	Andrew Neate	17/04/2025 09:02

There are 151 other versions that do you not have access to.

Question statement

Using the Table of Integrals/Antiderivatives, calculate the integral of $y=\simplify[unitFactor, unitPower,fractionNumbers]{{a_1}*x^{b_1}+{a_2}*x^{b_2}+{a_3}*x^{b_3}}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

a_1	integer	10
a_2	integer	4
a_3	integer	-9
b_1	rational	6/7
b_2	rational	1/7
b_3	rational	-5/8

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..10)

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:

Statement
Advice
"Unnamed part" → "Gap 0" - Correct answer

Parts

Gap-fill
1. Gap Gap 0 Mathematical expression
  Add

Gap-fill

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

Gap 0

Advice

From the Table of Integrals we see that a function of the form

$f(x)=x^n$ has the integral

$\int x^n dx = \frac{x^{n+1}}{n+1}+ c,$

and

$\int kf(x) dx = k \int f(x) dx.$

Additionally, the integral of the sum or difference of two or more functions is equal to the sum or difference of the integrals of each function:

$\int(f(x)\pm g(x))\, dx = \int f(x)\, dx \pm \int g(x) \, dx.$

So, for the function

$y=\simplify[all,fractionNumbers]{{a_1}*x^{b_1}+{a_2}*x^{b_2}+{a_3}*x^{b_3}},$

the integral is

$\begin{split}\simplify[all,fractionNumbers]{int({a_1}*x^{b_1}+{a_2}*x^{b_2}+{a_3}*x^{b_3},x)} = \simplify[all,fractionNumbers]{{a_1}int(x^{b_1},x)+{a_2}int(x^{b_2},x)+{a_3}int(x^{b_3},x)} &\,= \simplify[all,fractionNumbers,!collectNumbers,!simplifyFractions,!noLeadingMinus]{{a_1}(x^({b_1+1})/{b_1+1}) +{a_2}(x^({b_2+1})/{b_2+1}) +{a_3}(x^({b_3+1})/{b_3+1})} + c,\\ \\&\,= \simplify[all,fractionNumbers]{{a_1/(b_1+1)}x^{b_1+1}+{a_2/(b_2+1)}x^{b_2+1}+{a_3/(b_3+1)}x^{b_3+1}}+c.\end{split}$

Note: You only need to put one $c$ term here, you do not need to put a separate constant term for each calculation.

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

This question is not used in any exams.

Loading...

Error

Integration (Negative and Fractional Powers) 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 7 months ago

Ben McGovern 4 years ago

Ben McGovern 4 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Integration (Negative and Fractional Powers) 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 7 months ago

Ben McGovern 4 years ago

Ben McGovern 4 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`