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# intc

integral along a straight path in the complex plan

### Syntax

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

### Arguments

a, b
two complex numbers: starting and ending points of the integral in the complex plan.

f
Identifier of the function to be integrated.

abserr, relerr
real scalars: absolute and relative errors. Default values: `1.d-13` 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 plan.

### 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)```

• intg — definite integral
• intl — Cauchy integral

### History

 Version Description 5.5.0 Absolute and relative (input) and absolute (output) errors management added. 6.1.0 The default abserr value becomes 10-13 instead of 10-14.