What is the standard notation to express integration?

The standard notation to express integration is given by the symbol ∫ followed by the function being integrated, and the differential of the variable with respect to which the integration is performed (in this case, 'dx' for a function of 'x'). This notation signifies the process of calculating the integral of a function, providing a way to find the area under the curve described by the function over a specified interval or to find an antiderivative.

The notation ensures clarity in communicating that you are summing the infinitesimal contributions of the function 'f(x)' over all infinitesimal segments 'dx'. This is fundamental in calculus as it lays the groundwork for understanding more complex principles like definite and indefinite integrals.

In contrast, the other choices represent different mathematical processes: the first option, dy/dx, indicates the derivative of 'y' with respect to 'x', which is a completely different concept involving rates of change. The third option, ∑f(x), represents summation notation, usually applied in the context of finite sums rather than continuous integration. Finally, F(x) + c suggests an antiderivative form but does not denote the process of integration itself; it's more related to the result obtained from integration where 'F(x)' is