To determine

To use:

The midpoint rule to estimate the area of the wing’s cross section

Answer

Area =  4232 cm2

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:

Measurements of thickness of the wing in centimetres at 20 cm intervals

5.8, 20.3, 26.7, 29.0, 27.6, 27.3, 23.8, 20.5,15.1, 8.7,2.8

4) Calculation:

Let h(t)  denote the thickness of the wing at distance t from the left end.

From the given data, we take mid points at a distances 20 cm, 60 cm, 100 cm, 140 cm, and 180 cm from left side.

The corresponding thicknesses of the wing are  20.3, 29.0, 27.3, 20.5, 8.7.

Number of subintervals n=5

∆x= b-an  =200-05 = 40

Area = ∫0200htdt~∆x[20.3+29.0+27.3+20.5+8.7]

=4020.3+29.0+27.3+20.5+8.7=40(105.8)

Thus, area =  4232 cm2

Conclusion:

Area =  4232 cm2