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Interactive video lesson plan for: What makes an integral improper? (KristaKingMath)

Activity overview:

Improper integrals are a kind of definite integral, in the sense that we're looking for area under the function over a particular interval. This is in opposition to an indefinite integral, where we're looking for a function that represents the area everywhere under the function.

Sometimes people think that integrals are only defined as improper when the limits of integration are infinite (meaning that they are positive or negative infinity). While it's true that these are considered improper integrals, there are actually multiple ways that an integral can qualify as improper.

Integrals are improper when either the lower limit of integration is infinite, the upper limit of integration is infinite, or both the upper and lower limits of integration are infinite.

An integral is also considered improper if the integrand is discontinuous on the interval of integration, which means that the function we're integrating has a discontinuity in the interval. The discontinuity can also occur at either of the endpoints of the interval, or at both endpoints, and the function would still be considered to have a discontinuity in the interval, and would therefore still be an improper integral.

In this video we'll discuss exactly what it takes to make an integral improper.

● ● ● GET EXTRA HELP ● ● ●

If you could use some extra help with your math class, then check out Krista’s website // http://www.kristakingmath.com

● ● ● CONNECT WITH KRISTA ● ● ●

Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com

FACEBOOK // https://www.facebook.com/KristaKingMath
TWITTER // https://twitter.com/KristaKingMath
INSTAGRAM // https://www.instagram.com/kristakingmath/
PINTEREST // https://www.pinterest.com/KristaKingMath/
GOOGLE+ // https://plus.google.com/+Integralcalc/
QUORA // https://www.quora.com/profile/Krista-King

Tagged under: infinite limits integration,interval integration,integrals infinity,integrals infinity, ,infinite limits,infinity,integrals,Krista King,discontinuous integrand,integrand,calculus,upper limit,integration,educational, limit,improper integrals,negative infinity

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