# This worksheet contains the Maple commands from Chapter 15 of
# Introduction to Scientific Programming by Joseph L. Zachary.
# 
# (15.2)  This formula gives the cross section of the corrugated steel
# sheet discussed in Chapter 15.
# 
> f := 10 * sin(Pi*x/10)^2;
# 
# (15.3)  This is the first derivative of the formula from (15.2).
# 
> fprime := diff(f, x);
# 
# (15.10)  The int function will evaluate indefinite integrals.
# 
> int(sin(x)+2, x);
# 
# (15.11)  It will also evaluate definite integrals, if a range is
# associated with the variable of integration.
# 
> int(sin(x)+2, x=0.0..8.0);
# 
# (15.12)  The int function works symbolically, and it will sometimes
# fail to evaluate an integral, as in this case. 
# 
> int(sqrt(1 + fprime^2), x=0..10);
# 
# (15.13)  This combination of evalf and Int causes Maple to evaluate
# definite integrals using a numerical technique.
# 
> evalf(Int(sqrt(1 + fprime^2), x=0..10));
# 
# (15.14)  We use the integration package to animate the convergence of
# the rectangular method as it deals with the function sin(x) between 0
# and 8.  It generates 5 frames.  In the first frame 2 rectangles are
# used, and in each subsequent frame the number of rectangles doubles.
# 
> with(integration):
> animateRectangular((x) -> sin(x)+2, 0, 8, 5);
# 
# (15.20)  We use the integration package to animate the convergence of
# the trapezoidal method as it deals with the function sin(x) between 0
# and 8.  It generates 5 frames.  In the first frame 2 trapezoids are
# used, and in each subsequent frame the number of trapezoids doubles.
# 
> with(integration):
> animateTrapezoidal((x) -> sin(x)+2, 0, 8, 5);
>