Question

what does 'dx' signify in the integral and differentiation notation?
I was reading integration by substitution method where it is required to replace 'dx' and change the independent variable such that the integral could be transformed.I have read in derivatives that dx and dy are differential but I want
a little more explaination.someone please help me out

Answer 1

Since the integral is the area under the curve, consisting of a huge number od very skinny rectangles,

∫f(x) dx

is the sum of the areas of those rectangles, of height f(x) and width dx.

If you have to change variables, using u as a function of x, or x as a function of u, then you have to use the chain rule.

For example, if

x = u^2+3,
dx = 2u du

and so on