AP Calculus ABhardmcq1 pt

What is the total area of the regions enclosed by the graphs of $y=x^3$ and $y=3x^2-2x$ ?

0

\frac{1}{2}

\frac{1}{4}

1

Explanation

Core Concept

The curves intersect where $x^3=3x^2-2x$ , at $x=0,1,2$ . The area is $\int_0^1(x^3-3x^2+2x)\,dx+\int_1^2(3x^2-2x-x^3)\,dx=\frac{1}{4}+\frac{1}{4}=\frac{1}{2}$ .

Correct Answer

B $\frac{1}{2}$

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What is the total area of the regions enclosed by the graphs of y=x3y=x^3y=x3 and y=3x2−2xy=3x^2-2xy=3x2−2x?

Explanation

Core Concept

Correct Answer

More Unit 8: Applications of Integration practice questions

What is the total area of the regions enclosed by the graphs of $y=x^3$ and $y=3x^2-2x$ ?