Consider the definite integral I= _ -2 ^ 1 (x^ 3 -4x^ 2 +2 ) ,dx

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

Problem

Consider the definite integral

I=\int_{-2}^{1}\bigl(x^{3}-4x^{2}+2\bigr)\,dx.

Answer the questions below. (i) Determine an antiderivative

F(x)

of the integrand. (ii) Hence calculate the exact value of

I

. Show all steps clearly. (iii) Comment on the sign of your answer and interpret what it indicates about the area represented by the integral.