Simon's copy of Definite Integrals

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Simon Thomas 6 years, 1 month ago

Created this as a copy of Definite Integrals.

Name	Status	Author	Last Modified
Definite Integrals	draft	TEAME UCC	06/02/2017 13:31
Simple Definite Integrals	draft	Kieran Mulchrone	08/02/2017 14:37
Definite Integrals 1	draft	Violeta CIT	06/03/2017 16:34
Definite Integrals 1	draft	Violeta CIT	13/03/2017 09:12
Definite Integrals Exam Q1	draft	Violeta CIT	05/04/2017 16:36
Definite Integrals Exam Q2	draft	Violeta CIT	24/04/2017 12:56
Definite Integrals Exam Q3	draft	Violeta CIT	24/04/2017 12:58
Definite Integrals Exam Q4	draft	Violeta CIT	05/04/2017 16:39
Definite Integrals Exam Q5	draft	Violeta CIT	05/04/2017 16:42
Definite Integrals Exam Q6	draft	Violeta CIT	05/04/2017 16:44
Definite Integrals Exam Q6	draft	Violeta CIT	05/04/2017 16:57
Clodagh's copy of Definite Integrals Exam Q6	draft	Clodagh Carroll	24/04/2017 12:34
George's copy of Definite Integrals	draft	George Loughlin	06/07/2017 15:09
Definite Integrals [L9 Randomised]	Needs to be tested	Matthew James Sykes	25/07/2018 10:53
Johnny's copy of Definite Integrals	draft	Johnny Yi	01/11/2018 01:25
Simon's copy of Definite Integrals	draft	Simon Thomas	21/03/2019 09:23
Jo-Ann's copy of Definite Integrals	draft	Jo-Ann Lyons	25/04/2019 15:04
Musa's copy of 3 Definite Integrals - 1	draft	Musa Mammadov	27/06/2023 01:40

There are 8 other versions that do you not have access to.

Question statement

Evaluate the following definite integrals, giving your answer as a fraction as necessary.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	-2
c	integer	6
b	integer	2
d	integer	-2
g	integer	2
f	integer	3
h	integer	7
k	integer	1
j	integer	-4
l	integer	6

Automatically regenerate variables?

Name

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Value

xxxxxxxxxx
 
random(-4..0)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

-2

This variable doesn't seem to be used anywhere.

Advice

To evaluate a definite integral we must first integrate the function (we do not need to include c, the constant of integration) and then substitute in the given limits.

(a)

$\int_\var{a}^\var{b}(1 + \var{c}x)\mathrm{dx} = \left[x + \var{c/2}x^2\right]_\var{a}^\var{b}= [(\var{b})+ \var{c/2}(\var{b})^2]-[(\var{a}) + \var{c/2}(\var{a})^2]=\simplify{{b}+ {c/2}{b}^2-{a} - {c/2}{a}^2}$

(b)

$\int_\var{d}^\var{f} (x^2 + \var{g}x-\var{h})\mathrm{dx}= \left[\frac{x^3}{3} + \var{g/2}x^2-\var{h}x\right]_\var{d}^\var{f}=[\frac{(\var{f})^3}{3} + \var{g/2}(\var{f})^2-\var{h}(\var{f})]-[\frac{(\var{d})^3}{3} + \var{g/2}(\var{d})^2-\var{h}(\var{d})]=\var{f^3/3 + g/2*f^2-h*f-(d^3/3 + g/2*d^2-h*d)}$

(c)

$\int_\var{j}^\var{k}(x^3-\var{l}x^2)\mathrm{dx}=\left[\frac{x^4}{4} - \frac{\var{l}}{3}x^3\right]_\var{j}^\var{k}=[\frac{(\var{k})^4}{4} - \frac{\var{l}}{3}(\var{k})^3]-[\frac{(\var{j})^4}{4} - \frac{\var{l}}{3}(\var{j})^3]=\var{(k^4/4 - l/3*k^3)-(j^4/4 - l/3*j^3)}$

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This question is used in the following exams:

Introduction to Integration by Simon Thomas in Maths support.
Integration introduction by Simon Thomas in Calculus.

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Simon Thomas 6 years, 1 month ago

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Simon's copy of Definite Integrals

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 6 years, 1 month ago

Error in variable testing condition

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Warning

Generated value: integer

Parts

Number entry

Advanced settings

Generated value: `integer`