According to my knowledge dy/dx is not a ratio. Then while solving the problems of integration by substitution how can we use it as ratio. Because of we have dx/dt =f(x). Then while shoving it by substitution why do we take it as dx=dt•f(x).
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1It is a ratio of infinitesimals and so one has to be very careful as to applying the rules of algebra as if it were to be a fraction. +1 for the post. Please check the duplicate links. These answers are better than mine – imranfat Jul 19 '16 at 01:51