The command to use is shown below.
> int(x^2,x=0..4);
Notice that Maple gives an exact answer, as a fraction. If you want a decimal approximation to an integral, you just put an evalf command around the int command, as shown below.
> evalf(int(x^2,x=0..4));
To compute an indefinite integral with Maple, you just leave out the range for the limits of integration, as shown below.
> int(x^2,x);Note that Maple does not include a constant of integration.
You can also use the Maple int command with functions or expressions you have defined in Maple. For example, suppose you wanted to find area under the curve of the function on the interval . Then you can define this function in Maple with the command
> f := x -> x*sin(x);and then use this definition as shown below.
> int(f(x),x=0..Pi);
You can also simply give the expression corresponding to a label in Maple, and then use that label in subsequent commands as shown below. However, notice the difference between the two methods. You are urged you to choose one or the other, so you don't mix the syntax up.
> p := x*sin(x); > int(p,x=0..Pi);If you want to find the area bounded by the graph of two functions, you should first plot both functions on the same graph. You can then find the intersection points using either the solve or fsolve command. Once this is done, you can calculate the definite integral in Maple. An example below illustrates how this can be done in Maple by finding the area bounded by the graphs of and :
> f := x-> -x^2+4*x+6; > g := x-> x/3+2; > plot({f(x),g(x)},x=-2..6); > a := fsolve(f(x)=g(x),x=-2..0); > b := fsolve(f(x)=g(x),x=4..6); > int(f(x)-g(x),x=a..b);
> int(-16*t^2+100*t,t=1..5)/(5-1);
It is also easy to use Maple to compute centroids and centers of mass. For example, suppose you wanted to compute the coordinates of the centroid of the region bounded above by the curve and below by the axis over the interval . The first thing to do is to plot the region.
> q := -3*x^2+3*x+36; > plot(q,x=-3..4);Once you have plotted the region, you can compute the area with the following command. Note the use of a label, since we'll use the area later.
> area := int(q,x=-3..4);Once we have the area, we can compute and as follows.
> x_bar := int(x*q,x=-3..4)/area; > y_bar := int(q^2,x=-3..4)/(2*area);A similar procedure can be used to find the centroid of a region in the plane that is bounded by the graphs of two functions. You just have to use the following formulas for and .
> ?FresnelSTo obtain a numerical approximation to the integral, just put an evalf command on the outside of the int command.