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Merge pull request #217 from lambda-feedback/tr186-add-integral-as-elementary-function
Removed ~ since it causes issues with Github markdown formatting
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‎app/docs/user.md

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@@ -148,24 +148,24 @@ Note that the function treats radians and steradians as dimensionless values.
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| radian | r | $(2\pi)^{-1}$ |
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| steradian | sr | $(4\pi)^{-1}$ |
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| hertz | Hz | $\mathrm{second}^{-1}$ |
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| newton | N | $\mathrm{metre}~\mathrm{kilogram}~\mathrm{second}^{-2}$ |
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| pascal | Pa | $\mathrm{metre}^{-1}~\mathrm{kilogram}~\mathrm{second}^{-2}$ |
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| joule | J | $\mathrm{metre}^2~\mathrm{kilogram~second}^{-2}$ |
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| watt | W | $\mathrm{metre}^2~\mathrm{kilogram~second}^{-3}$ |
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| coulomb | C | $\mathrm{second~ampere}$ |
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| volt | V | $\mathrm{metre}^2~\mathrm{kilogram second}^{-3}~\mathrm{ampere}^{-1}$ |
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| farad | F | $\mathrm{metre}^{-2}~\mathrm{kilogram}^{-1}~\mathrm{second}^4~\mathrm{ampere}^2$ |
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| ohm | O | $\mathrm{metre}^2~\mathrm{kilogram second}^{-3}~\mathrm{ampere}^{-2}$ |
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| siemens | S | $\mathrm{metre}^{-2}~\mathrm{kilogram}^{-1}~\mathrm{second}^3~\mathrm{ampere}^2$ |
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| weber | Wb | $\mathrm{metre}^2~\mathrm{kilogram~second}^{-2}~\mathrm{ampere}^{-1}$ |
161-
| tesla | T | $\mathrm{kilogram~second}^{-2} \mathrm{ampere}^{-1}$ |
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| henry | H | $\mathrm{metre}^2~\mathrm{kilogram~second}^{-2}~\mathrm{ampere}^{-2}$ |
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| newton | N | $\mathrm{metre} \mathrm{kilogram} \mathrm{second}^{-2}$ |
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| pascal | Pa | $\mathrm{metre}^{-1} \mathrm{kilogram} \mathrm{second}^{-2}$ |
153+
| joule | J | $\mathrm{metre}^2 \mathrm{kilogram second}^{-2}$ |
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| watt | W | $\mathrm{metre}^2 \mathrm{kilogram second}^{-3}$ |
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| coulomb | C | $\mathrm{second ampere}$ |
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| volt | V | $\mathrm{metre}^2 \mathrm{kilogram second}^{-3} \mathrm{ampere}^{-1}$ |
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| farad | F | $\mathrm{metre}^{-2} \mathrm{kilogram}^{-1} \mathrm{second}^4 \mathrm{ampere}^2$ |
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| ohm | O | $\mathrm{metre}^2 \mathrm{kilogram second}^{-3} \mathrm{ampere}^{-2}$ |
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| siemens | S | $\mathrm{metre}^{-2} \mathrm{kilogram}^{-1} \mathrm{second}^3 \mathrm{ampere}^2$ |
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| weber | Wb | $\mathrm{metre}^2 \mathrm{kilogram second}^{-2} \mathrm{ampere}^{-1}$ |
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| tesla | T | $\mathrm{kilogram second}^{-2} \mathrm{ampere}^{-1}$ |
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| henry | H | $\mathrm{metre}^2 \mathrm{kilogram second}^{-2} \mathrm{ampere}^{-2}$ |
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| lumen | lm | $\mathrm{candela}$ |
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| lux | lx | $\mathrm{metre}^{-2}~\mathrm{candela}$ |
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| lux | lx | $\mathrm{metre}^{-2} \mathrm{candela}$ |
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| becquerel | Bq | $\mathrm{second}^{-1}$ |
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| gray | Gy | $\mathrm{metre}^2~\mathrm{second}^{-2}$ |
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| sievert | Sv | $\mathrm{metre}^2~\mathrm{second}^{-2}$ |
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| katal | kat | $\mathrm{mole~second}^{-1}$ |
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| gray | Gy | $\mathrm{metre}^2 \mathrm{second}^{-2}$ |
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| sievert | Sv | $\mathrm{metre}^2 \mathrm{second}^{-2}$ |
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| katal | kat | $\mathrm{mole second}^{-1}$ |
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###### Table: Common non-SI units
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@@ -176,52 +176,52 @@ Note that only the first table in this section has short form symbols defined, t
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| Unit name | Symbol | Expressed in SI units |
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|-------------------|:-------|:-------------------------------------------|
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| minute | min | $60~\mathrm{second}$ |
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| hour | h | $3600~\mathrm{second}$ |
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| minute | min | $60 \mathrm{second}$ |
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| hour | h | $3600 \mathrm{second}$ |
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| degree | deg | $\frac{1}{360}$ |
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| liter | l | $10^{-3}~\mathrm{metre}^3$ |
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| metric_ton | t | $10^3~\mathrm{kilogram}$ |
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| liter | l | $10^{-3} \mathrm{metre}^3$ |
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| metric_ton | t | $10^3 \mathrm{kilogram}$ |
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| neper | Np | $1$ |
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| bel | B | $\frac{1}{2}~\ln(10)$ |
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| electronvolt | eV | $1.60218 \cdot 10^{-19}~\mathrm{joule}$ |
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| atomic_mass_unit | u | $1.66054 \cdot 10^{-27}~\mathrm{kilogram}$ |
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| angstrom | å | $10^{-10}~\mathrm{metre}$ |
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| bel | B | $\frac{1}{2} \ln(10)$ |
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| electronvolt | eV | $1.60218 \cdot 10^{-19} \mathrm{joule}$ |
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| atomic_mass_unit | u | $1.66054 \cdot 10^{-27} \mathrm{kilogram}$ |
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| angstrom | å | $10^{-10} \mathrm{metre}$ |
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| Unit name | Expressed in SI units |
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|------------------|:-----------------------------------------------------|
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| day | $86400~\mathrm{second}$ |
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| day | $86400 \mathrm{second}$ |
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| angleminute | $\frac{\pi}{10800}$ |
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| anglesecond | $\frac{\pi}{648000}$ |
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| astronomicalunit | $149597870700~\mathrm{metre}$ |
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| nauticalmile | $1852~\mathrm{metre}$ |
197-
| knot | $\frac{1852}{3600}~\mathrm{metre~second}^{-1}$ |
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| are | $10^2~\mathrm{metre}^2$ |
199-
| hectare | $10^4~\mathrm{metre}^2$ |
200-
| bar | $10^5~\mathrm{pascal}$ |
201-
| barn | $10^{-28}~\mathrm{metre}$ |
202-
| curie | $3.7 \cdot 10^{10}~\mathrm{becquerel} |
203-
| roentgen | $2.58 \cdot 10^{-4}~\mathrm{kelvin~(kilogram)}^{-1}$ |
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| rad | $10^{-2}~\mathrm{gray}$ |
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| rem | $10^{-2}~\mathrm{sievert}$ |
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| astronomicalunit | $149597870700 \mathrm{metre}$ |
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| nauticalmile | $1852 \mathrm{metre}$ |
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| knot | $\frac{1852}{3600} \mathrm{metre second}^{-1}$ |
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| are | $10^2 \mathrm{metre}^2$ |
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| hectare | $10^4 \mathrm{metre}^2$ |
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| bar | $10^5 \mathrm{pascal}$ |
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| barn | $10^{-28} \mathrm{metre}$ |
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| curie | $3.7 \cdot 10^{10} \mathrm{becquerel} |
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| roentgen | $2.58 \cdot 10^{-4} \mathrm{kelvin (kilogram)}^{-1}$ |
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| rad | $10^{-2} \mathrm{gray}$ |
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| rem | $10^{-2} \mathrm{sievert}$ |
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###### Table: Imperial units
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Commonly imperial units taken from [Wikipedia, Imperial Units](https://en.wikipedia.org/wiki/Imperial_units)
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| Unit name | Symbol | Expressed in SI units |
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|-------------------|:-------|:----------------------------------------------|
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| inch | in | $0.0254~\mathrm{metre}$ |
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| foot | ft | $0.3048~\mathrm{metre}$ |
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| yard | yd | $0.9144~\mathrm{metre}$ |
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| mile | mi | $1609.344~\mathrm{metre}$ |
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| fluid ounce | fl oz | $28.4130625~\mathrm{millilitre}$ |
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| gill | gi | $142.0653125~\mathrm{millilitre}$ |
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| pint | pt | $568.26125~\mathrm{millilitre}$ |
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| quart | qt | $1.1365225~\mathrm{litre}$ |
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| gallon | gal | $4546.09~\mathrm{litre}$ |
222-
| ounce | oz | $28.349523125~\mathrm{gram}$ |
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| pound | lb | $0.45359237~\mathrm{kilogram}$ |
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| stone | st | $6.35029318~\mathrm{kilogram}$ |
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| inch | in | $0.0254 \mathrm{metre}$ |
214+
| foot | ft | $0.3048 \mathrm{metre}$ |
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| yard | yd | $0.9144 \mathrm{metre}$ |
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| mile | mi | $1609.344 \mathrm{metre}$ |
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| fluid ounce | fl oz | $28.4130625 \mathrm{millilitre}$ |
218+
| gill | gi | $142.0653125 \mathrm{millilitre}$ |
219+
| pint | pt | $568.26125 \mathrm{millilitre}$ |
220+
| quart | qt | $1.1365225 \mathrm{litre}$ |
221+
| gallon | gal | $4546.09 \mathrm{litre}$ |
222+
| ounce | oz | $28.349523125 \mathrm{gram}$ |
223+
| pound | lb | $0.45359237 \mathrm{kilogram}$ |
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| stone | st | $6.35029318 \mathrm{kilogram}$ |
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#### `plus_minus` and `minus_plus`
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@@ -295,7 +295,7 @@ There are three examples in the example problem set. Each examples uses an EXPRE
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##### Example (a)
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The response area below has answer `2.00 km/h` $2.00~\frac{\mathrm{kilometre}}{\mathrm{hour}}$ .
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The response area below has answer `2.00 km/h` $2.00 \frac{\mathrm{kilometre}}{\mathrm{hour}}$ .
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There are many possible correct responses, e.g. `2.00 kilometre/hour`, `2 km/h`, `2000 m/h`, `0.556 meter/second`, `2 metre/millihour`.
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@@ -608,12 +608,12 @@ Some more feedback customisation is shown in *Examples: Customizing comparison u
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#### Using integrals
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The evaluation function can handle one-dimensional definite integrals, i.e. expression in the form $\int_a^b f(x)~\mathrm{d}x$, if the `elementary\\\_functions` parameter is set to true. The integrand and the boundary values can be symbolic.
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The evaluation function can handle one-dimensional definite integrals, i.e. expression in the form $\int_a^b f(x) \mathrm{d}x$, if the `elementary_functions` parameter is set to true. The integrand and the boundary values can be symbolic.
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**Note:** Indefinite integrals (expression in the form $\int f(x)~\mathrm{d}x$), contour integrals ($\oint f(x)~\mathrm{d}x$) and integrals based on abstract measures ($\int_A f(x)~\mathrm{d}\mu$) are not supported.
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**Note:** Indefinite integrals (expression in the form $\int f(x) \mathrm{d}x$), contour integrals ($\oint f(x) \mathrm{d}x$) and integrals based on abstract measures ($\int_A f(x) \mathrm{d}\mu$) are not supported.
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The expression $\int_a^b f(x)~\mathrm{d}x$ can be written `Integral(f(x), (x, a, b))`. The syntax works as follows: the integral sign corresponds to `Integral` (the short form `int` can also be used), which must be followed by two argument, first is the integrand (the function that is integrated), the second is a triple containing; the variable to be integrated over and the two boundary values.
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The expression $\int_a^b f(x) \mathrm{d}x$ can be written `Integral(f(x), (x, a, b))`. The syntax works as follows: the integral sign corresponds to `Integral` (the short form `int` can also be used), which must be followed by two argument, first is the integrand (the function that is integrated), the second is a triple containing; the variable to be integrated over and the two boundary values.
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Here is an example of an integral that can be fully evaluated, more specifically $\int_0^2 3xy~\mathrm{d}x = 6y$. If the answer is set to `Integral(3xy, (x, 0, 2))` then response area will accept both integral expressions, e.g. `int(3*y*x, (x, 0, 2))`, and computed expressions, e.g. `6y`.
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Here is an example of an integral that can be fully evaluated, more specifically $\int_0^2 3xy \mathrm{d}x = 6y$. If the answer is set to `Integral(3xy, (x, 0, 2))` then response area will accept both integral expressions, e.g. `int(3*y*x, (x, 0, 2))`, and computed expressions, e.g. `6y`.
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The boundary and function does not need to be defined explicitly. As an example of a more abstract integral we can consider $\int_a^b f(x)+g(x)~\mathrm{d}x$. If the answer is set to `Integral(f(x)+g(x), (x, a, b))` then, for example, `int(g(x)+f(x), (x, a, b))` $\int_a^b g(x)+f(x)~\mathrm{d}x$ and `int(f(x), (x, a, b)) + int(g(x), (x, a, b))` $\int_a^b f(x)~\mathrm{d}x+\int_a^b g(x)~\mathrm{d}x$.
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The boundary and function does not need to be defined explicitly. As an example of a more abstract integral we can consider $\int_a^b f(x)+g(x) \mathrm{d}x$. If the answer is set to `Integral(f(x)+g(x), (x, a, b))` then, for example, `int(g(x)+f(x), (x, a, b))` $\int_a^b g(x)+f(x) \mathrm{d}x$ and `int(f(x), (x, a, b)) + int(g(x), (x, a, b))` $\int_a^b f(x) \mathrm{d}x+\int_a^b g(x) \mathrm{d}x$.

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