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November 20th, 2017, 11:32 PM  #1 
Newbie Joined: Apr 2016 From: Wonderland Posts: 18 Thanks: 0  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? 
November 21st, 2017, 12:48 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,731 Thanks: 1808 
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.

November 21st, 2017, 04:58 PM  #3 
Newbie Joined: Apr 2016 From: Wonderland Posts: 18 Thanks: 0  
November 22nd, 2017, 01:13 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,731 Thanks: 1808 
Yes... for x = 1, x²/2 + C$_1$ = x + C$_2$, so C$_1$ = 1.5 + C$_2$ is needed.


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discontinuous, function, integrating 
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