int — Evaluate scalar symbolic indefinite and definite integrals.
int(expr) returns an indefinite integral with respect to the first symbolic variable in expr. int(expr, var) chooses the variable explicitly. int(expr, a, b) and int(expr, var, a, b) evaluate definite integrals by substituting the bounds into the antiderivative.
Syntax
F = int(expr)
F = int(expr, var)
F = int(expr, a, b)
F = int(expr, var, a, b)Inputs
| Name | Type | Required | Default | Description |
|---|---|---|---|---|
expr | Any | Yes | — | Scalar symbolic or numeric expression to integrate. |
var | Any | No | symvar(expr, 1) | Integration variable as a symbolic variable or text scalar. |
a | Any | No | — | Lower integration bound. |
b | Any | No | — | Upper integration bound. |
Returns
| Name | Type | Description |
|---|---|---|
F | Any | Scalar symbolic indefinite or definite integral result. |
Errors
| Identifier | When | Message |
|---|---|---|
RunMat:int:InvalidExpression | The expression cannot be represented as a scalar symbolic expression. | int: expected a scalar symbolic or numeric expression |
RunMat:int:InvalidVariable | The integration variable cannot be inferred or is not a symbolic variable/text scalar. | int: invalid symbolic variable |
RunMat:int:InvalidBound | A definite integration bound cannot be represented as a scalar symbolic expression. | int: invalid integration bound |
RunMat:int:InvalidOption | A name-value option is unknown or its value is not scalar. | int: invalid option |
RunMat:int:ArgCount | The argument grammar does not match int(expr), int(expr,var), int(expr,a,b), or int(expr,var,a,b). | int: invalid number of input arguments |
How int works
- Default variable selection follows the scalar symbolic
symvar(expr, 1)rule used by MATLAB-compatible calculus builtins:xis preferred when present, then remaining valid symbolic names are considered in deterministic lexical order. - Supported closed forms include constants, variables, sums, differences, scalar multiples, powers of the integration variable, reciprocal
1/x,sin,cos,exp,log(x), andsqrt(x). - Definite integrals simplify numeric trigonometric and exponential bounds when the antiderivative can be evaluated.
- Unsupported symbolic forms return a formal symbolic
int(...)expression instead of failing, preserving downstream symbolic workflows. - The MATLAB name-value options
IgnoreAnalyticConstraints,PrincipalValue,IgnoreSpecialCases, andHoldare accepted for scalar compatibility. RunMat currently ignores them for the supported elementary subset.
Examples
Integrate a polynomial
syms x
F = int(x^2)Expected output:
F = x^3/3Evaluate a definite integral
syms x
A = int(sin(x), 0, pi)Expected output:
A = 2Choose the integration variable explicitly
syms x y
F = int(y, x)Expected output:
F = x*yUsing int with coding agents
Open a RunMat example with live inputs, then ask the agent to explain how int changes the result.
Run a small int example, explain the result, then change one input and compare the output.
FAQ
Does int run on the GPU?⌄
No. Symbolic expressions are host algebra values. Numeric tensors should use numerical integration routines when available.
What happens when RunMat cannot find a closed form?⌄
RunMat returns a formal scalar symbolic int(...) expression so code can continue to manipulate or display the unevaluated integral.
Related Math functions
Elementwise
abs · angle · bsxfun · complex · conj · double · erf · erfcinv · exp · expm1 · factorial · flintmax · gamma · gammaln · heaviside · hypot · idivide · imag · intmax · intmin · ldivide · log · log10 · log1p · log2 · minus · nextpow2 · plus · pow2 · power · rdivide · real · realmax · realmin · realsqrt · rescale · sign · single · sqrt · swapbytes · times · uint32
Trigonometry
acos · acosh · asin · asinh · atan · atan2 · atanh · cos · cosd · cosh · cospi · deg2rad · pol2cart · rad2deg · sin · sind · sinh · sinpi · tan · tand · tanh
Reduction
all · any · bounds · cummax · cummin · cumprod · cumsum · cumtrapz · diff · gradient · max · maxk · mean · median · min · mink · movmax · movmean · movmedian · movmin · movprod · movstd · movsum · movvar · nnz · prod · rms · std · sum · trapz · var
Structure
bandwidth · isdiag · ishermitian · issymmetric · istril · istriu · symrcm
Signal
blackman · butter · buttord · cheb2ord · conv · conv2 · deconv · downsample · envelope · filter · filtfilt · fir1 · freqz · gauspuls · hamming · hann · hilbert · periodogram · pulstran · pwelch · rectpuls · resample · sawtooth · sinc · spectrogram · square · tripuls · unwrap · upsample · zplane
Optim
coneprog · fminbnd · fminunc · fsolve · fzero · integral · linprog · lsqcurvefit · lsqnonlin · optimset · quad · secondordercone
Ops
cross · ctranspose · dot · mldivide · mpower · mrdivide · mtimes · pagemtimes · pagetranspose · trace · transpose
Open-source implementation
Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how int is executed, line by line, in Rust.
- View the source for int in Rust on GitHub
- Learn how the RunMat runtime works
- Found a bug? Open an issue with a minimal reproduction.
About RunMat
RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.
- RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
- Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.