# integral should not be zero

```
F = sqrt((cos(x) - 1)^2 + sin(x)^2)
F.integrate(x, 0, 2*pi)
```

yields 0, the expected answer is 8.

integral should not be zero

```
F = sqrt((cos(x) - 1)^2 + sin(x)^2)
F.integrate(x, 0, 2*pi)
```

yields 0, the expected answer is 8.

add a comment

1

Indeed.

```
sage: F.nintegrate(x,0,2*pi)
(8.0, 8.881784197001255e-14, 21, 0)
```

Maxima does this correctly internally.

```
(%i2) integrate( sqrt((cos(x) - 1)^2 + sin(x)^2), x, 0, 2*%pi);
(%o2) 8
```

But

```
(%i5) load(abs_integrate);
(%o5) /Users/.../sage/local/share/maxima/5.34.1/share/contr\
ib/integration/abs_integrate.mac
(%i6) integrate( sqrt((cos(x) - 1)^2 + sin(x)^2), x, 0, 2*%pi);
(%o6) 0
```

So this seems to be a bug in that package.

1

This is now tracked at http://trac.sagemath.org/ticket/17183 and reported upstream at https://sourceforge.net/p/maxima/bugs/2823/ .

Asked: **
2014-10-19 17:44:26 -0500
**

Seen: **179 times**

Last updated: **Oct 20 '14**

Stack overflow in boolean test

integral() failing with "segmentation fault"

$p$-adic regulator calculations

Sage incorrectly evaluates series

Convert exponential form to hyperbolic functions

Sage symbolic math simplification error

Sagemath 8.0 and Sagemath 8.1 and Windows 10

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.