#### To determine

**To use:**

The midpoint rule to estimate the area of pool

#### Answer

91.2 m2

#### Explanation

**1) Concept:**

Use the midpoint rule to evaluate the area.

**2) Midpoint rule**

∫abfx dx=∑i=1nfxi∆x= ∆x ( f(x1)+fx2+…+f xn)

where ∆x= b-an and xi is a midpoint of [xi-1 , xi]

**3) Given:**

Figure showing widths of a kidney shaped swimming tank

**3) Calculation:**

Choose n =4, and draw rectangles showing the midpoints.

x = distance from left end pool

w = w(x) = width at x

The midpoints are at a distance 2 m,6 m, 10 m, and 14 m from the left end.

The corresponding widths are 6.2, 6.8, 5.0, 4.8 respectively.

∆x= b-an =82-04 = 4

Using midpoint rule,

Area = ∫016wxdx~ ∆x (6.2+6.8+5.0+4.8)

=46.2+6.8+5.0+4.8

=91.2 m2

Thus, area = 91.2m2

**Conclusion:**

Area of the pool =91.2 m2