MATH137 Lecture Notes - Lecture 12: Paula Smith, Antiderivative, Riemann Sum

• School: University of Waterloo
• Department: Mathematics
• Course: MATH137
• Professor: Catherine Briggs

Document Summary

Math 137 week 12 notes dr. paula smith. When we studied derivatives, we first looked at f (a), the derivative of the function f at a specific point (a number), before we considered f (x), the derivative of f at any point (a function). Similarly, we first considered the definite integral, a f(x) dx, which is a number, before we turn to the indefinite integral, f(x) dx, which, we will see, is a function. From the ftc part ii, a x f(t) dt = f(x) . F(a) = f(x) + c, since f(a) is a number. If we choose not to consider the lower limit, f(a) might be anything, and x is already a variable. An important idea is used here: f(x) dx = f (x) dx = f(x) + c, i. e. , the integral of the derivative of f is the original f plus a constant.