For definite integration, the `int`

command restricts the integration
variable `x`

to the given range of integration.

int(sin(ln(x)), x = 0..5)

If the `int`

command
determines that an integral does not converge, it returns the special
value `undefined`

:

int(exp(x*I), x = 1..infinity)

When the `int`

command
cannot compute an integral and also cannot prove that the integral
does not converge, it returns an unresolved integral:

int(sin(cos(x)), x = 0..10)

For definite integrals, the `int`

command restricts the integration
to the specified interval. If you use the `assume`

function to set properties on
the integration variable, `int`

temporarily
overwrites these properties and integrates over the specified interval.
To display warnings, set the value of `intlib::printWarnings`

to `TRUE`

:

intlib::printWarnings(TRUE): assume(x > 0): int(x, x = 1 .. 2); int(x, x = -3 .. 1)

Warning: The assumption that 'x' has property 'Dom::Interval([1], [2])' instead of given property 'Dom::Interval(0, infinity)' is used for integration. [int]

Warning: The assumption that 'x' has property 'Dom::Interval([-3], [1])' instead of given property 'Dom::Interval(0, infinity)' is used for integration. [int]

After computing an integral, MuPAD^{®} restores the assumptions
set for integration variable. If you do not want the assumptions to
affect further computations, use the `unassume`

function:

unassume(x)

MuPAD also makes implicit assumptions on the specified
interval. Suppose, you use the integration range as `[a, b]`

.
The system assumes that both `a`

and `b`

represent
real numbers, and that `a <= b`

unless you clearly
specify otherwise. If you set the value of `intlib::printWarnings`

to `TRUE`

, MuPAD displays
the warning about using implicit assumptions:

int(heaviside(x - a), x = a..b)

Warning: Cannot decide if 'a <= b' is true, will temporarily assume it is true. [int]

To avoid this implicit assumption, specify that ```
a >
b
```

or `a < b`

int(heaviside(x - a), x = a..b) assuming a > b

int(heaviside(x - a), x = a..b) assuming a < b

For further computations, disable the warnings:

intlib::printWarnings(FALSE):

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