∫ (integral)

Performs numerical integration.

Syntax

• ∫(expr, var, a, b[, Δ])

  • expr is an expression in one variable var

  • var is the variable in expr

  • a is the lower bound

  • b is the upper bound

  • Δ is the resolution of the integration (step size of var)

Description

∫ performs numerical integration of a real-valued function of a single real variable on a finite interval.

Notes

If the optional resolution argument Δ isn’t specified, the resolution is chosen so that the interval will be divided into 100 000 parts of the same width. Hence, the default value of Δ is abs(b − a) / 100000.

Decreasing Δ might improve the accuracy of the computed definite integral, but it will always make the computation take longer to complete.

Examples

∫(x^2, x, 0, 1)

0.33333333335

∫(sin(x), x, 0, π)

1.99999999984

∫(sech(x), x, −100, 100)

3.14159265359	(=π)

∫(e^−(x^2), x, −10, 10)

1.77245385091	(=√π)

2⋅∫(√(1−x^2), x, −1, 1)

3.14159254841

∫(x^2, x, 0, 1, 1/10000000)

0.333333333333

See also

• integrate (synonym)