AP Calculus ABhardmcq1 pt

What is the total area of the regions between the graph of y=x36x2+8xy=x^3-6x^2+8x and the xx-axis on the interval [0,4][0,4]?

A.88
B.00
C.44
D.1616

Explanation

Core Concept

The curve factors as x(x2)(x4)x(x-2)(x-4) and is positive on (0,2)(0,2), negative on (2,4)(2,4). The area is 02(x36x2+8x)dx+24(x36x2+8x)dx=4+4=8\int_0^2(x^3-6x^2+8x)\,dx+\int_2^4-(x^3-6x^2+8x)\,dx=4+4=8.

Correct Answer

A88

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