MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
The region U is enclosed by the curve y=ln(x+1), the x-axis, and the vertical lines x=0 and x=3. The region is revolved about the horizontal line y=4.
(a) For 0≤x≤3, express the distances from the line y=4 to the top and bottom of the region as functions of x.
(b) Write a definite integral that represents the volume of the solid obtained from the revolution.
(c) Evaluate the integral in part (b) to three decimal places.