Let be an even

MATHEMATICS · Single correct · AP · Calculus BC · Applications of Integration · Applications of Integration

Problem

Let

g

be an even, differentiable function on

[-3,3]

. Which of the following expressions gives the length of the graph of

y=g(x)

[-3,3]

? (a)

\displaystyle\int_{-3}^{3}\sqrt{1+\bigl(g(x)\bigr)^{2}}\,dx

(b)

\displaystyle 2\int_{0}^{3}\lvert g'(x)\rvert\,dx

(c)

\displaystyle 2\int_{0}^{3}\sqrt{1+\bigl(g'(x)\bigr)^{2}}\,dx

(d)

\displaystyle\int_{0}^{3}\sqrt{1+\bigl(g'(x)\bigr)^{2}}\,dx