Let S be the region in the –plane bounded on the right by the curve
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Let S be the region in the xy–plane bounded on the right by the curve x=y2+1, on the left by the y–axis, below by the horizontal line y=−2, and above by y=3.
(1) Set up, but do not evaluate, an integral expression whose value equals the exact area of region S.
(2) Evaluate the integral from part (a) to obtain an exact numerical value for the area.
(3) Compute a decimal approximation of the area correct to three decimal places.
(4) Interpret the meaning of the area you found in part (b) in terms of accumulated horizontal "slices"; specifically, explain what each differential element represents geometrically.