Integration: Using a Table of Integrals 5b

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Christian Lawson-Perfect 2 years, 6 months ago

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Ben McGovern 4 years, 8 months ago

Created this as a copy of Integration: Using a Table of Integrals 5a.

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
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Differentiation: Stationary Points and their Nature 1	Ready to use	Ben McGovern	26/09/2022 11:56
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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
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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
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Integration: By Substitution 1a ii (Negative and Fractional Powers)	Ready to use	Ben McGovern	27/09/2022 09:01
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There are 151 other versions that do you not have access to.

Question statement

Using the Table of Integrals/Antiderivatives, calculate the integral of $f(x)=\simplify[unitFactor]{{a}cos({b}x)}.$

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			a	integer	2
			b	integer	7

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

$f(x)= \cos(nx)$ has the integral

$\int \cos(nx) dx = \frac{1}{n}\sin(nx)+c,$

and

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

So, for the function

$f(x)=\simplify{{a}cos({b}x)},$

the integral is

$\begin{split} \int\simplify{{a}cos({b}x)} dx \,= \simplify[unitFactor]{{a}int(cos({b}x),x)} &\,=\simplify[unitFactor]{{a}(1/{b} sin({b}x))} +c, \\ &\,=\simplify[unitFactor,fractionNumbers]{{a/b} sin({b}x)+c}. \end{split}$

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This question is used in the following exams:

Integration using a Table of Integrals by Ben McGovern in MASH Bath: Moodle quizzes and TS.
Week 13 e-quiz by Ruth Douglas in Ruth's workspace.
All the good stuff by Chris Templet in Chris's workspace.
Integration by recognition by Jinhua Mathias in Maths 3-2020.
Summer Quiz 4 by Kate Vincent in Kate's workspace.
Quiz 4 by Kate Vincent in Kate's workspace.
Calculus by Morgiane Richard in Mathematics for Geosciences.
Review of Formulas and Techniques by ahmad mustafa in ahmad's workspace.

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Christian Lawson-Perfect 2 years, 6 months ago

Ben McGovern 4 years ago

Ben McGovern 4 years, 8 months ago

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Integration: Using a Table of Integrals 5b

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 6 months ago

Ben McGovern 4 years ago

Ben McGovern 4 years, 8 months ago

Error in variable testing condition

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Warning

Generated value: integer

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Generated value: `integer`