To estimate: The area of cross section of airplane wing
The area of cross section of airplane wing is .
The thickness is measured each 20 cm interval.
The general expression for Midpoint Rule is shown below:
The interval width is (1)
The midpoint is (2)
Here, width of the subinterval is , the upper limit is b, the lower limit is a, the number of subinterval is n, and the midpoint of is .
Find the width of the subinterval using Equation (1) as shown below.
Consider the number of subintervals as 5.
Substitute 5 for n, 200 cm for b, and 0 for a in Equation (1).
Let the distance from the left end of the wing be x.
The height of the wing at x is .
The expression to find the area of the pool for the width to with using midpoint rule is shown below.
Here, the height of the wing at distance is , the height of the wing at distance is , the height of the wing at distance is , the height of the wing at distance is , and the height of the wing at distance is .
The end points of the distance intervals are 0, 40 cm, 80 cm, 120 cm, 160 cm, and 200 cm.
The midpoints of the intervals are 20 cm, 60 cm, 100 cm, 140 cm, and 180 cm.
Substitute 40 cm for , 20 cm for , 60 cm for , 100 cm for , 140 cm for , and 180 cm for in Equation (3) as shown below.
Substitute 20.3 cm for , 29.0 cm for , 27.3 cm for , 20.5 cm for , and 8.7 meter for in Equation (4) as shown below.
Therefore, the area of cross section of airplane wing is .
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