In math, the integral operator is represented by the integral symbol and typically appears in an expression like this.
In plain language, this means to take the integral of the function with respect to along the range from to .
An integral has four parts: the expression being integrated, the differential, a start value and an end value. The differential indicates which variable we are integrating over.
When a start and end value are included the integral is called a definite integral since the author is expressing that they want to calculate the result of the integral.
When there is no start and end value the integral is called an indefinite integral.
To read more about computing both definite and indefinite integrals see this page.
The first derivative of a function is denoted by an apostrophe after the function name. Alternatively, the partial symbol can be used to represent the derivative with respect to a variable.
An antiderivative of a function f(x) is represented by a function F(x) such that the derivative of F(x) is f(x). Essentially, an antiderivative reverses the process of differentiation.