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- Surfacearea is
ImproperIntegrals
LearningObjectives
A studentwill be able to:
- Computeby handthe integralsof a wide varietyof functionsby usingthe techniqueof ImproperIntegration.
- Combinethis techniquewith otherintegrationtechniquesto integrate.
- Distinguishbetweenproperand improperintegrals.
The conceptof improperintegralsis an extensionto the conceptof definiteintegrals.The reasonfor the
termimproperis becausethoseintegralseither - includeintegrationover infinitelimitsor
- the integrandmay becomeinfinitewithinthe limitsof integration.
We will take eachcaseseparately. Recallthat in the definitionof definiteintegral we assume
that the intervalof integration is finiteand the function is continuouson this interval.
IntegrationOverInfiniteLimits
If the integrand is continuousover the interval then the improperintegralin this caseis defined
as