Calculate the total wind force on the building by using the trapezoidal rule.

Question

A wind force distributed against the side of a skyscraper (the height of the

building is 240 m) is measured as (the force is shown as force per unit height)

Calculate the total wind force on the building by using the trapezoidal rule.

 

Answer 1

Step 1:

Total wind force on the building is , where  is the force exerted by the buliding at a height .

The Height of the building is 240 m.

Find using trapeziodal rule.

Let us consider number of subintervals : .

Trapezoidal Rule:

Let be continuous on . The Trapezoidal Rule for approximating is given by

,

where and  .

.

Observe the table and substitute the corresponding values.

Using Trapezoidal Rule, .

Solution :

.