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## Main Question or Discussion Point

How is it possible that one can break up the derivative operator such as this:

[tex]\frac{dv}{dt}=t^2[/tex], then integrate like this,

[tex] \int^v_{v_{0}}dv = \int^t_0 t^2 dt [/tex], where[tex] v=v_{o} [/tex] when [tex]t=0[/tex]. Especially in light of what most calculus teachers tell you; that the derivative symbol is not a fraction and should not be interpreted as a faction?

[tex]\frac{dv}{dt}=t^2[/tex], then integrate like this,

[tex] \int^v_{v_{0}}dv = \int^t_0 t^2 dt [/tex], where[tex] v=v_{o} [/tex] when [tex]t=0[/tex]. Especially in light of what most calculus teachers tell you; that the derivative symbol is not a fraction and should not be interpreted as a faction?