Apentix/AP Calculus AB/Unit 8: Applications of Integration/Question

AP Calculus ABmediummcq1 pt

What is the total area of the regions enclosed by the graphs of $y=x^3$ and $y=x$ on the interval $[-1,1]$ ?

A.

0

B.

\frac{1}{4}

C.

1

D.

\frac{1}{2}

Explanation

Core Concept

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

Correct Answer

D $\frac{1}{2}$

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