A correction to the definition of ∫f(x)dx
Welcome file Abstract . This essay points out a widely appeared mistake in some textbooks about the definition of the indefinite integral notation ∫ f ( x ) dx \int_{}^{}{f\left( x \right)\text{dx}} ∫ f ( x ) dx . Some textbooks define ∫ f ( x ) dx \int_{}^{}{f\left( x \right)\text{dx}} ∫ f ( x ) dx as a set of antiderivatives of f f f , such as Thomas’Calculus 1 : The collection of all antiderivatives of f f f is called the indefinite integral of f f f with respect to x x x , and is denoted by ∫ f ( x ) dx \int_{}^{}{f\left( x \right)\text{dx}} ∫ f ( x ) dx The symbol ∫ \int_{}^{}{} ∫ is an integral sign. The function f f f is the integrand of the integral, and x x x is the variable of integration. And also in another widely used book James Stewart’s Calculus 2 : …an indefinite integral ∫ f ( x ) dx \int_{}^{}{f\left( x \right)\text{dx}} ∫ f ( x ) dx is a function (or family of functions )… Be aware of the phrase enclosed in th...