Let, y = y(x)
Differentiation dy/dx is defined as Lt ( Δx → 0 ) ( (y(x + Δx ) - y(x)) / Δx ).
Where Δx = small increment of x .
A function is differentiable on a point only if it is continuous at that point [ Because we have to have the value of y(x) to differentiate ].
Differentiation gives the slope of a function at certain point . [ See any standard book for prove ]
While integration is the anti-differentiation . i.e ∫ (dydx)dx = y + c [ c is arbitrary constant ]
Definition of inegration : g(x) = ∫ f(x)dx iff dg/dx = f
While the physical significance of integration is the definite integration and its explanation as Riemann Integral http://en.wikipedia.org/wiki/Riemann_integral .
Differentiation dy/dx is defined as Lt ( Δx → 0 ) ( (y(x + Δx ) - y(x)) / Δx ).
Where Δx = small increment of x .
A function is differentiable on a point only if it is continuous at that point [ Because we have to have the value of y(x) to differentiate ].
Differentiation gives the slope of a function at certain point . [ See any standard book for prove ]
While integration is the anti-differentiation . i.e ∫ (dydx)dx = y + c [ c is arbitrary constant ]
Definition of inegration : g(x) = ∫ f(x)dx iff dg/dx = f
While the physical significance of integration is the definite integration and its explanation as Riemann Integral http://en.wikipedia.org/wiki/Riemann_integral .
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