Which of the following definite integrals gives the exact arc length of the graph of…

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

Problem

Which of the following definite integrals gives the exact arc length of the graph of a differentiable function y=f(x)y=f(x) on the interval [a,b][a,b]? (a) ∫ab(1+(f′(x))2) dx\displaystyle \int_a^b \bigl(1+\bigl(f'(x)\bigr)^2\bigr)\,dx (b) ∫ab1+(f(x))2 dx\displaystyle \int_a^b \sqrt{1+\bigl(f(x)\bigr)^2}\,dx (c) ∫ab1+(f′(x))2 dx\displaystyle \int_a^b \sqrt{1+\bigl(f'(x)\bigr)^2}\,dx (d) ∫ab∣f′(x)∣ dx\displaystyle \int_a^b \lvert f'(x)\rvert\,dx

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