Area under a parabola

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Johnny Yi 5 years, 11 months ago

Created this as a copy of Jo-Ann's draft copy of Area under a curve by integration.

Name	Status	Author	Last Modified
Area under a curve by integration	Ready to use	William Haynes	01/01/2021 00:48
haifa's copy of Area under a curve by integration	draft	haifa abd	17/10/2018 14:32
Blathnaid's copy of Area under a curve by integration	draft	Blathnaid Sheridan	12/11/2018 13:17
Blathnaid's copy of Blathnaid's copy of Area under a curve by integration	draft	Blathnaid Sheridan	12/11/2018 13:17
William's copy of Area under a curve by integration	draft	William Lee	15/11/2018 15:47
Johnny's copy of William's copy of Area under a curve by integration	draft	Johnny Yi	10/12/2018 05:50
Ann's copy of Area under a curve by integration	draft	Ann Smith	15/01/2019 13:09
Jo-Ann's copy of Area under a curve by integration	draft	Jo-Ann Lyons	17/04/2019 14:20
Jo-Ann's draft copy of Area under a curve by integration	draft	Jo-Ann Lyons	25/04/2019 15:22
Area under a parabola	draft	Johnny Yi	30/04/2019 04:06
Maria's copy of Jo-Ann's draft copy of Area under a curve by integration	draft	Maria Aneiros	27/05/2019 07:21
Area under a curve by integration	draft	Xiaodan Leng	10/07/2019 23:20
Anna's copy of Area under a curve by integration	draft	Anna Strzelecka	11/07/2019 17:45

There are 11 other versions that do you not have access to.

Question statement

Given the function $\color{red}{y=\simplify[!noleadingminus,unitfactor]{{A} x^2 + {B} x + {C}}}$ , determine the area under the curve from the y-axis to the point where the curve crosses the positive x-axis. The x- and y- coordinates are in [{units}]. Give your answers correct to at least 3 significant figures and include the correct units (nb: if you see 'in' or 'mm' etc. it means inches, millimetres etc. Write the units as they appear in the question).

{geogebra_applet('nuhzkzqp',[['a',A],['b',B],['c',C]])}

Give any introductory information the student needs.

			Name	Type	Generated Value

A	number	-1.5
B	integer	1
C	number	1.5
root1	quantity	quantity(1.387425886722793, "ft")
area	quantity	quantity(1.708250985247548, "ft^2")
units	string	ft
debug	boolean	false

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-0.5..-2#0.5)

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: `number`

-1.5

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Engineering Accuracy with units
  Add
2. Gap Gap 1. Engineering Accuracy with units
  Add
Part b) Gap-fill
1. Gap Engineering Accuracy with units
  Add

Gap-fill

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

Determine the points where the curve crosses the axes.

$h$ = Gap 0. {qty(C,units)}

$a$ = Gap 1. {siground(root1,4)}

Advice

To find the point where the curve crosses the y-axis, set x = 0 and solve for y.
To find the point where the curve crosses the positive x-axis, set y to zero and solve for x using the quadratic formula.
To find the area under the curve, divide the shaded area into vertical differential strips where $dA = y\, dx$ then integrate between the horizontal limits to find the area.

$\begin{align}A &= \int dA \\&= \int_0^a y\,dx \\&= \int_0^a(\simplify[!noleadingminus,unitfactor]{{A} x^2 + {B} x + {C}})\, dx\\& = \left[ \simplify[unitfactor,collectnumbers]{{A} x^3/3 + {B} x^2/3 + {C}x}\right]_0^\var{scalar(siground(root1,4))}\\&=\var{siground(area,4)}\end{align}$

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Johnny Yi 5 years, 11 months ago

Error in variable testing condition

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Warning

Generated value: `number`

Parts

Gap-fill

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Area under a parabola

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Johnny Yi 5 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`