Generate Constants of Integration & Summation

Integrate can now generate an arbitrary constant for indefinite integrals. While this is a part of standard calculus, the arbitrary functions that appear in higher dimensions for multiple integrals, sums and products may be surprising at a first glance.

Generate an arbitrary constant for an indefinite integral.

This represents a family of curves in the plane.

Generate arbitrary functions for a multiple indefinite integral.

Verify the result using D.

Generate an arbitrary constant for an indefinite sum.

Verify the result using DifferenceDelta, which is the discrete derivative.

Generate an arbitrary constant for an indefinite product.

Verify the result using DiscreteRatio, which is the inverse for indefinite products.

Generate arbitrary functions for a multiple indefinite sum.

Generate arbitrary functions for a multiple indefinite product.