For a smooth curve defined by on

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

Problem

For a smooth curve defined by

y=f(x)

[a,b]

, which of the following definite integrals gives the length of the curve between

x=a

and

x=b

? (a)

\displaystyle \int_{a}^{b} \bigl(1+[f'(x)]^{2}\bigr)\,dx

(b)

\displaystyle \int_{a}^{b} \sqrt{1+[f'(x)]^{2}}\,dx

(c)

\displaystyle \int_{a}^{b} |f'(x)|\,dx

(d)

\displaystyle \int_{a}^{b} \sqrt{1+[f(x)]^{2}}\,dx