Let be defined on the closed interval .

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

f(x)=x^{2}-4

be defined on the closed interval

[-3,3]

. (i) Determine the points where the graph of

y=f(x)

intersects the

x

-axis. (ii) Without evaluating any integrals, explain why the definite integral

\int_{-3}^{3}f(x)\,dx

does not represent the numerical (unsigned) area bounded by the curve and the

x

-axis over

[-3,3]

. (iii) Write, but do not evaluate, the integral or integrals whose numerical value equals the required area.