Recognise and apply a standard integral - random coefficients version

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Question statement

Let $f(x) = \simplify{ {c[0]} * e^({k}x) + {c[1]} * x^{k} + {c[2]} * cos({k}x) + {c[3]}*sin({k}x) }$ .

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			Name	Type	Generated Value

			c	list	[ 0, 0, 0, 1 ]
			k	integer	9

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shuffle([1,0,0,0])

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Generated value: `list`

[ 0, 0, 0, 1 ]

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"Unnamed part" - Correct answer
"Unnamed part" → "Forgot constant of integration" - Correct answer
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"Unnamed part" → "Differentiated - constant of integration" - Correct answer

Advice

$f(x) = \simplify{ {c[0]} * e^({k}x) + {c[1]} * x^{k} + {c[2]} * cos({k}x) + {c[3]}*sin({k}x) }$ .

The integral of $\simplify{ {c[0]} * e^(k*x) + {c[1]} * x^k + {c[2]} * cos(k*x) + {c[3]}*sin(k*x)}$ is $\simplify{ {c[0]} * (1/k) * e^(k*x) + {c[1]} (1/(k+1))* x^(k+1) + {c[2]} * (1/k) * sin(k*x) - {c[3]}* 1/k * cos(k*x)}$

This is an indefinite integral, so we add an arbitrary constant of integration $C$ .

Here, $k = \var{k}$ , so

$\int f(x) \, \mathrm{d}x = \simplify{{c[0]} * (1/{k}) * e^({k}x) + {c[1]} * (1/{k+1}) * x^{k+1} + {c[2]} * 1/{k} * sin({k}x) + {c[3]} * -1/{k}*cos({k}x)} + C$

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Recognise and apply a standard integral - random coefficients version

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Recognise and apply a standard integral - random coefficients version

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 4 years, 7 months ago

Christian Lawson-Perfect 4 years, 7 months ago

Christian Lawson-Perfect 4 years, 7 months ago

Error in variable testing condition

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Generated value: list

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

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Variables

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Generated value: `list`