Essential Knowledge 3.2C3

Essential Knowledge 3.2C3 Students will know that the definition of the definite integral may be extended to functions with removable or jump discontinuities.

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As we saw in the last section, you can take two adjacent integrals and add them together. I'll repeat it here.

Integral of a Function of Adjacent Integrals

Rule

Example

Given

and

Then

So what does this mean for us as far as removable or jump discontinuities? Well, the example kinda says it all. Let's say we want to find the integral from 2 to 10, but there is a removable or jump discontinuity at 5 stopping us. No problem, just do the integral from 2 to 5, then from 5 to 10, then add the two integrals together and you're good. Not much more to say.