Example 6.2

Given Area = $\int _{2}^{5} x^{2}dx$ , an analytical solution would produce 39. Use trapz command and solve it

1. Initialize variable x as a row vector, from 2 with increments of 0.1 to 5: x=2:.1:5;
2. Declare variable y as y=x^2;. Note the following error prompt : ??? Error using ==> mpower Inputs must be a scalar and a square matrix.
This is because x is a vector quantity and MATLAB is expecting a scalar input for y. Because of that, we need to compute y as a vector and to do that we will use the dot operator as follows: y=x.^2;. This tells MATLAB to create vector y by taking each x value and raising its power to 2.
3. Now we can issue the following command to calculate the ﬁrst area, the output will be as follows:

    area1=trapz(x,y)
area1 =
    39.0050

Notice that this numerical value is slightly off. So let us increase the number of increments and calculate the area again:

    x=2:.01:5;
y=x.^2;
area2=trapz(x,y)

area2 =
    39.0001

Yet another increase in the number of increments:

    x=2:.001:5;
y=x.^2;
area3=trapz(x,y)

area3 =
    39.0000

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