Let A(x)= 13(x-1)^3+2 and B(x)= x^ 3 3 -x^ 2 +x+5

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

A(x)=\tfrac13(x-1)^3+2\quad\text{and}\quad B(x)=\tfrac{x^{3}}{3}-x^{2}+x+5.

(a) Verify that

A

and

B

are antiderivatives of the same function on

\mathbb R

. (b) Determine the numerical value of

B(x)-A(x)