Changes

The '''definite integral''' is a very important concept for students wishing to learn multivariate calculus, as we define many different kinds of definite integrals in this course.   

The '''definite integral''' is a very important concept for students wishing to learn multivariate calculus, as we define many different kinds of definite integrals in this course.   

Let <math>f(x) \ </math> be any function associating real numbers with real numbers, and let the [[Closed set|closed interval]] <math>[a,b] \ </math> be in the domain of the function.  Let's divide this interval into <math>n \ </math> smaller intervals, so that the first one is <math>[a,q_1] \ </math> and the last one is <math>[q_{n-1},b] \ </math>, and for convenience we'll call <math>a = q_0, b=q_n \ </math>.  Furthermore, let's pick a point in each of these intervals, say <math>x_j \in [q_{n-1},q_n] \ </math>.  Now we form the sum

Let <math>f(x) \ </math> be any function associating real numbers with real numbers, and let the [[Closed set|closed interval]] <math>[a,b] \ </math> be in the domain of the function.  Let's divide this interval into <math>n \ </math> smaller intervals, so that the first one is <math>[a,q_1] \ </math> and the last one is <math>[q_{n-1},b] \ </math>, and for convenience we'll call <math>a = q_0, b=q_n \ </math>.  Furthermore, let's pick a point in each of these intervals, say <math>x_j \in [q_{n-1},q_n] \ </math>.  Now we form the sum