# This worksheet contains the Maple commands from Chapter 15 of 
# Introduction to Scientific Programming by Joseph L. Zachary.
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# 
# (15.2)  This formula gives the cross section of the corrugated steel sheet 
# discussed in Chapter 15.
# 
> f := 10 * sin(Pi*x/10)^2;
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# 
# (15.3)  This is the first derivative of the formula from (15.2).
# 
> fprime := diff(f, x);
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# 
# (15.10)  The "int" function will evaluate indefinite integrals.
# 
> int(sin(x)+2, x);
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# 
# (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);
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# 
# (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);
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# 
# (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));
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# 
# (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 rectrangles doubles.
# 
> with(integration):\
animateRectangular((x) -> sin(x)+2, 0, 8, 5);
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# 
# (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);
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>