Area under the curve - below x-axis - Numbas at mathcentre.ac.uk

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Jinhua Mathias

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Jinhua Mathias

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Ready to use

7 years, 11 months ago

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Jinhua Mathias 7 years, 11 months ago

Gave some feedback: Ready to use

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Jinhua Mathias 8 years, 2 months ago

Created this as a copy of Jinhua's copy of Area under the curve - below x-axis.

Name	Status	Author	Last Modified
Area under the curve - above x-axis	Ready to use	joshua boddy	01/06/2016 09:47
Area under the curve - below x-axis	Ready to use	joshua boddy	01/06/2016 09:47
Jinhua's copy of Area under the curve - above x-axis	Ready to use	Jinhua Mathias	28/08/2024 12:15
Jinhua's copy of Area under the curve - below x-axis	Ready to use	Jinhua Mathias	28/08/2024 12:15
Area under the curve - below x-axis	Ready to use	Jinhua Mathias	27/08/2024 16:37
Area under the curve - above x-axis	Ready to use	Jinhua Mathias	27/08/2024 16:37
Area under the curve - below x-axis	draft	Xiaodan Leng	11/07/2019 05:12
Area under the curve - above x-axis	draft	Xiaodan Leng	11/07/2019 05:12

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Question statement

{eqnline(a,b,x2,y2)}

You are given a quadratic graph of $\simplify{y =-x^2+({a}+{b})x-{a}{b}}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	5
x2	integer	-3
b	integer	1
y2	integer	8
c	integer	3
ans	number	-24.6666666667

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random(-4..5 except 0)

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Generated value: `integer`

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Advice

Recall that the area under a curve $f(x)$ between $x=a$ and $x=b$ is given by $\int^b_a f(x) \mathrm{d}x$

Hence we calculate $\int^\var{y2}_\simplify{{a}+1} (\simplify{-x^2+({a}+{b})x-{a}{b}}) \mathrm{d}x = \simplify[all,fractionnumbers]{(-({y2})^3/3+({a}+{b})({y2})^2/2-{a}{b}({y2}))-(-({a}+1)^3/3+({a}+{b})({a}+1)^2/2-{a}{b}({a}+1))={ans}}$

Note that the area under the curve is always positive yet out answer here is negative, so we must remember to multiply our answer by $-1$

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Area under the curve - below x-axis

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Jinhua Mathias 7 years, 11 months ago

Jinhua Mathias 8 years, 2 months ago

Error in variable testing condition

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Generated value: `integer`

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Error

Area under the curve - below x-axis

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Jinhua Mathias 7 years, 11 months ago

Jinhua Mathias 8 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `integer`