Give an example of a function that is integrable on the interval [-1,1], but not continuous on [-1,1]. explain.

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Fabian

Mathematics

3 December, 23:10

Give an example of a function that is integrable on the interval [-1,1], but not continuous on [-1,1]. explain.

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Curry · Answer 1

With an absolute value somewhere in the formula, you can create a discontinuous function.

how about f (x) = |x|/x

It jumps from - 1 to + 1 at x=0, yet it can be integrated on [-1,1]. The surface is 2.