MATHEMATICS · Multi-part · AP · Calculus BC · Applications of Integration · Applications of Integration
Problem
Consider the curve defined by x=31y23 for 0≤y≤4.
(a) Write, but do not yet evaluate, a definite integral whose value equals the length of the curve between the points where y=0 and y=4. Clearly indicate the limits of integration.
(b) Evaluate the integral exactly to obtain a closed-form expression for the length. Show all algebraic and calculus steps used to simplify the integrand and to compute the antiderivative.
(c) Use appropriate arithmetic to provide the length to three decimal places. Clearly state the units of measure implied by your calculation.