Let F(x)= _ 0 ^ x (3t^ 2 -4t+1 ) ,dt

MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

F(x)=\int_{0}^{x} \bigl(3t^{2}-4t+1\bigr)\,dt.

Answer the following. (a) Calculate

F'(x)

. (b) Evaluate

F'(2)

. (c) Determine the exact value of

F(2)

. Show all steps in your calculation.