#### 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.

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.