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November 21st, 2017, 12:32 AM   #1
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Integrating a discontinuous function

For this piecewise function,

f(x) = -x for x > -1
-1 for x < -1

Let's say F(x) is the integral of f(x).

At x = -1, is F(x) a discontinuous point, corner, or a tangent?

I believe F(x) is a discontinuous point as I integrated f(x) respectively. As a result, I got -x^2/2 for x > -1
and -x for x < -1
So if I substitute -1 in, I get 2 different values, so there should be a discontinuity. However, I am told that it's a corner. Why?
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November 21st, 2017, 01:48 AM   #2
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You need to choose the constants of integration in such a way that the indefinite integral is continuous. It then has a corner at x = -1.
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November 21st, 2017, 05:58 PM   #3
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Hi Skipjack,

Do you mean something like this?

https://imgur.com/a/5dZyo
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November 22nd, 2017, 02:13 PM   #4
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Yes... for x = -1, -x²/2 + C$_1$ = -x + C$_2$, so C$_1$ = 1.5 + C$_2$ is needed.
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