Program 43

K.Dzwonkiewicz

C++

 

Consider the graph of the function f(x)=5x³

 

 

 

 

 

 

This graph increases as it moves right. We need to find the area under the curve from the y-axis to x=2. This area is contained within a region that has 3 sides that are straight lines, but the fourth side is a curve. We can cut the area up into little rectangles whose sum approaches the exact area. The more rectangles that are used the greater the accuracy. We will store the area in the cells of apvector. When done finding the last area, add the individual areas to get the approximate area.

 

Ask the boundaries: start... 0   to end...2

Ask how many rectangles: amt= 10

Width of one rectangle: end/amt = .2

Area of first: L x H or (width) x f(x)        .2 x 5(.2)³ = .008

Area of second:                                  .2 x 5(.4)³ =.064

Area of third:                                      .2 x 5(.6)³ = .216

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Area of tenth:                                      .2 x 5(2)³ = 8.00

 

Sum of ten rectangles:      24.2000

Run your program for 10, 100, 1000, and 10000 rectangles

The actual area is 20 square units from taking the integral.

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