Question

so I'm trying to figure out how chemical engineers use the application of integration by parts in their daily job, and maybe an example of how they would use it? please and thank you so much

Answer 1

Differential equations, which are equations that relate functions with their derivatives, and there are analytic methods to solve that use integration, as well as numerical integrator.

DEs are everywhere in our lives. Light can be described by a wave equation, and similarly quantum particles (in your computer, for instance) are also described by a [slightly different] wave equation. Anywhere where there is water flowing can be described by a DE. Aerodynamics, vibrations, propulsion, electronics, sprinklers, traffic jams, population growth and decay, image processing, machine vision, neural networks, weather, heat transfer, engine efficiency, climate change, structural integrity, nuclear weapons, artillery trajectory, solar cells, financial derivatives pricing.