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# intc

Cauchy integral

### Syntax

`[y  [,err]] = intc(a, b, f [,abserr [,relerr]])`

### Arguments

a, b

two complex scalars

f

"external" function

abserr, rerr

real scalars, absolute and relative errors. Default values: `1.d-14` and `1d-8`.

err

real number, estimated absolute error on the result.

### Description

If `f` is a complex-valued function, `intc(a, b, f)` computes the integral from `a` to `b` of `f(z)dz` along the straight line `[a b]` of the complex plane.

### Examples

```function y=f(z)
y = z^(3 + %pi * %i);
endfunction

intc(1+%i, 4-%i, f)

[r, err] = intc(1+%i, 4-%i, f, 1d-10, 1d-6)```

### See also

• intg — definite integral
• intl — Cauchy integral

### History

 Version Description 5.5.0 Absolute and relative (input) and absolute (output) errors management added.
 Report an issue << int3d Differential calculus, Integration integrate >>

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