MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
Consider the function F(x)=xln∣x∣−x defined for x=0.
(a) Show that F′(x)=ln∣x∣ for x=0.
(b) Using part (a), write the general antiderivative of ln∣x∣.
(c) Determine the value of the constant of integration if the antiderivative passes through the point (1,0).
(d) Comment on the continuity of the antiderivative obtained in part (c) at x=0.