Which integral represents the exact length of the graph of on the interval ?

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

Problem

Which integral represents the exact length of the graph of

y=x^{3}

on the interval

0\le x\le 2

? (a)

\displaystyle \int_{0}^{2}\sqrt{1+3x^{2}}\,dx

(b)

\displaystyle \int_{0}^{2}\bigl(1+9x^{4}\bigr)\,dx

(c)

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

(d)

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