Integration (Negative and Fractional Powers) 1

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Created this as a copy of Integration: Using a Table of Integrals 1.

Name	Status	Author	Last Modified
Differentiation: Using a Table of Derivatives 1	Ready to use	Ben McGovern	05/04/2023 11:25
Differentiation (Harder powers - negative and fractions) 1	draft	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 1	Ready to use	Ben McGovern	27/09/2022 09:01
Integration (Negative and Fractional Powers) 1	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Definite Integrals 1	Ready to use	Ben McGovern	31/08/2023 14:51
CB1 Differentiate Polynomials 1	Ready to use	Mash Sheffield	17/04/2025 09:02

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Question statement

Using the Table of Integrals/Antiderivatives, calculate the integral of $y=\simplify[all,fractionNumbers]{{a}x^{b/c}}$ .

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			Name	Type	Generated Value

a	integer	-5
b	integer	2
c	integer	5

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Generated value: `integer`

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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

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

So, for the function

$y=\simplify[fractionNumbers]{{a}x^{b/c}},$

the integral is

$\begin{split}\simplify[fractionNumbers]{int({a}x^{b/c},x)} = \simplify[fractionNumbers]{{a}int(x^{b/c},x)}&\,= \simplify[all,fractionNumbers,!collectNumbers,!simplifyFractions,!expandBrackets]{{a}({c/(b+c)}x^({b/c+1}))} + c,\\ \\&\,= \simplify[all,fractionNumbers]{{a/(b/c+1)}x^{b/c+1}}+c.\end{split}$

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This question is used in the following exams:

Integration Basic by Jinhua Mathias in Maths 3-2020.
Quiz 4 by Kate Vincent in Kate's workspace.
Subject Knowledge Homework 2 by Ciaran Cassidy in A Level Subject Knowledge Homework.

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Integration (Negative and Fractional Powers) 1

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Christian Lawson-Perfect 2 years, 7 months ago

Ben McGovern 4 years ago

Ben McGovern 4 years, 8 months ago

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Integration (Negative and Fractional Powers) 1

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

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Warning

Generated value: integer

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Generated value: `integer`