Presentation Title

Integration by the Wrong Parts

Start Date

November 2016

End Date

November 2016

Location

HUB 302-#17

Type of Presentation

Poster

Abstract

When using the calculus technique of integration by parts ((integral
of u dv) = uv - (integral of v du)), one must decide what the "parts"
u and dv will be. Usually one choice leads to an integral that is
simpler than the original, but the "wrong" choice leads to a more
complicated integral. In calculus classes we are taught that making
the wrong choice is a bad idea, so making the wrong choice over and
over again seems like a very bad idea that is doomed to failure.
However, in a recent article entitled "Integration by the Wrong
Parts," Bill Kronholm outlines a technique in which integration by
parts is applied infinitely many times, each time using the "wrong"
choice of u and dv, to obtain an infinite series representing the
answer to the integral. We show in detail how Kronholm's technique can
be used to integrate functions such as x*sin(x) and x*cos(x) in a very
unconventional way.

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Integration by the Wrong Parts

HUB 302-#17

When using the calculus technique of integration by parts ((integral
of u dv) = uv - (integral of v du)), one must decide what the "parts"
u and dv will be. Usually one choice leads to an integral that is
simpler than the original, but the "wrong" choice leads to a more
complicated integral. In calculus classes we are taught that making
the wrong choice is a bad idea, so making the wrong choice over and
over again seems like a very bad idea that is doomed to failure.
However, in a recent article entitled "Integration by the Wrong
Parts," Bill Kronholm outlines a technique in which integration by
parts is applied infinitely many times, each time using the "wrong"
choice of u and dv, to obtain an infinite series representing the
answer to the integral. We show in detail how Kronholm's technique can
be used to integrate functions such as x*sin(x) and x*cos(x) in a very
unconventional way.