CAS MA 123 Lecture Notes - Lecture 29: J-Ax, Antiderivative, Differentiable Function

• School: Boston University
• Department: Mathematics & Statistics
• Course: CAS MA 123
• Professor: John Bergdall

Document Summary

Suppose f(x) is a function on an open interval i then an antiderivative f(x) for f(x) is a differentiable function f(x) on i and f"(x) = f(x) F(x) = x2 is an antiderivative of f(x) = l(x) on i (- , ) f(x) = 2x also has an antiderivative f(x) = 2x + 13. If f(x) and g(x) differentiable on interval i such that f"(x) = g"(x) on i then there is a constant c such that g(x) = f(x) + c. If f(x) is an antiderivative of f(x) on an interval i any other antiderivatives of f(x) on i is of the form f(x) + c, c is constant. F(x) = sinx is an antiderative of f(x) = cosx. 1+x2 has f(x) = tan-1x as one antiderivative. F ( x) dx = indefinite intergral of f(x) with respect to x. Sin ( x) dx = -cos(x) + c. F(x) = -1/x is an antiderivative for f(x)= 1/x2.