Calculus/Integrals

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Expert: - 2/4/2008


Question
A rectangular swimming pool is 30 ft wide and 50 ft long. The table below shows the depth h(x) of the water 5-ft intervals from one end of the pool to the other. Estimate the volume of water in the pool using (a) left-endpoints values and (b) right-endpoint values.
Position(ft)   Depth(ft)   Position (ft)     Depth(ft)   
x               h(x)       x                 h(x)   
0               6          30                11.5
5               8.2        35                11.9
10              9.1        40                12.3
15              9.9        45                12.7
20              10.5       50                13
25              11

Answer
Draw the figures on a graph.  Between each two points, a trapezoid can be drawn.  Some shortcuts can be taken.  For example, the trapezoid between 20 and 25 has the same slope as the one between 25 and 30.  There is another one (or maybe more).

Find the area by
 the width * (sum of the two sides) / 2
for each trapezoid.

The sum of all the areas is the answer.

Calculus

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