Integration: Definite Integrals 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

Ready to use

4 years ago

History

○

Ben McGovern 2 years, 7 months ago

Published this.

○

Ben McGovern 4 years ago

Gave some feedback: Ready to use

○

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

Evaluate

$\int_{\var{n_1}}^{\var{n_2}}\simplify[unitFactor, unitPower, fractionNumbers]{{a_1}*x^{b_1}+{a_2}*x^{b_2}+{a_3}*x^{b_3}} \,dx.$

Give any introductory information the student needs.

			Name	Type	Generated Value

			Name	Type	Generated Value

a_1	integer	2
a_2	integer	-3
a_3	integer	-6
b_1	integer	3
b_2	integer	2
b_3	integer	1
n_1	integer	1
n_2	integer	3
eval2	number	-13.5
eval1	number	-3.5
eval2a	number	-13.500
eval1a	number	-3.500
sol	number	-10
sol1	number	-10.00

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..5)

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:

eval1
eval2

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 (Give answers to 2 decimal places where necessary)

Advice

Integrating a function of the form

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

$\int_a^b x^n dx = \left[\frac{x^{n+1}}{n+1}\right]_a^b,$

and

$\int_a^b kf(x) dx = k \int_a^b f(x) dx.$

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:

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

Therefore,

$\begin{split}\simplify[unitFactor,unitPower]{defint({a_1}*x^{b_1}+{a_2}*x^{b_2}+{a_3}*x^{b_3},x,{n_1},{n_2})} &\,= \simplify{{a_1}defint(x^{b_1},x,{n_1},{n_2})+{a_2}defint(x^{b_2},x,{n_1},{n_2})+{a_3}defint(x^{b_3},x,{n_1},{n_2})} \\ &\,= \left[\simplify[all,fractionNumbers]{{a_1}x^{b_1+1}/{b_1+1}+{a_2}x^{b_2+1}/{b_2+1}+{a_3}x^{b_3+1}/{b_3+1}}\right]_\var{n_1}^\var{n_2} \\ &\,= \left[\simplify[all,fractionNumbers,!collectNumbers]{{a_1*n_2^(b_1+1)}/{b_1+1}+{a_2*n_2^(b_2+1)}/{b_2+1}+{a_3*n_2^(b_3+1)}/{b_3+1}}\right] -\left[\simplify[all,fractionNumbers,!collectNumbers]{{a_1*n_1^(b_1+1)}/{b_1+1}+{a_2*n_1^(b_2+1)}/{b_2+1}+{a_3*n_1^(b_3+1)}/{b_3+1}}\right] \\ &\,= \simplify[!collectNumbers]{{eval2a}-{eval1a}} \\ &\,=\var{sol1} \end{split}$

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 used in the following exams:

Integration: Definite Integrals by Ben McGovern in MASH Bath: Moodle quizzes and TS.
Integration - Definite Integrals by Yousuf Ibrahim in Yousuf's workspace.
Integration Basic by Jinhua Mathias in Maths 3-2020.
Basic integration and finding area using integration by Jinhua Mathias in Maths 3-2020.
FS0031 Unit 5 Practice CLE Week 2 by Hannah Lerman in FS0031 Unit 5.
All the good stuff by Chris Templet in Chris's workspace.
Week 14 e-quiz by Ruth Douglas in Ruth's workspace.
FS0031 Unit 5 CLE 2 22-23 by Hannah Lerman in FS0031 Unit 5.
22-23 FS0031 Resit CLE by Doug Satterford in FS0031 Unit 5.
Summer Quiz 4 by Kate Vincent in Kate's workspace.
Sam's copy of Integration - Definite Integrals - Worksheet by Sam jemison in Sam's workspace.
Quiz 4 by Kate Vincent in Kate's workspace.
Subject Knowledge Homework 2 by Ciaran Cassidy in A Level Subject Knowledge Homework.
Calc Practice by S Russell in S's workspace.
23-24 FS0031 Resit CLE by Doug Satterford in FS0031 Unit 5.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben McGovern 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: Definite Integrals 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben McGovern 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`