Say a particle is traveling along the parameterized curve $\left(X,Y\right)$, where $X$ and $Y$ are functions of time. I want to find the distance it has traveled as a function of time. The solution would be something like this: $$\int_0^t\sqrt{\dot{X}^2+\dot{Y}^2}\,dt$$ This integral is with respect to $t$, and the integral is on the interval $[0,t]$. Is it correct to have $t$ in both places? I would like to avoid using another variable.
A quick question regarding integral notation.
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integration
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0I don't think this is a question. If you don't want to use another symbol what can the answer tell you? – 2017-01-27
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0Not really... I'd either leave the bounds blank or use different bounds or variables. – 2017-01-27
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1It is incorrect, though $[t_0, t_1]$ is a common standard. – 2017-01-27
1 Answers
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It's not correct. You're forcing $t$ to have an out-of-body experience. It has to go to $0$ and travel back to itself. There's no getting out of a new variable.
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0Okay, thank you for your help :) – 2017-01-27
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1This is my new favorite way of describing this error. – 2017-01-27