1340ForShowA27.mws
Thu Oct 27 13:08:55 MDT 2005

>

restart:

Page 98 of our Text -- Integration

Antiderivatives:    via Maple

>	Int( cos(2*x) , x);

>

value(%);

Maple doesn't do "+ C"

Nobody knows a nice Calculus-I antiderivative for :

>	Int(  exp(-x^2), x);   value(%);

Or for  

>	Int(  exp(sec(x^2)), x);   value(%);

Definite integrals :

>	rex := Int( tan(x), x=0..Pi/4);

>	value(rex); evalf(%);

>	rex := Int( tan(x), x=0..Pi);  value(rex);

>	rex := Int( tan(x), x=0..Pi/2);  value(rex);

The derivative of  -- FTC-I in Chapter 5 of 170 text

>	F := unapply(   Int( u^3 - 2*u, u=0..x),  x);

>

D(F);

Section 7.1:

We now calculate the area under the graph of  from -1 to 2:

>	f := x -> exp(-x^2);

>	XRG := -1..2:

>	Area := Int( f(x) , x=XRG);

>	evalf( value(Area));

Maybe we should plot first to make sure we aren't missing something:

>	plot(f,XRG);

Now go for the area:

>	value(Area);

Broaden the integration range:

>	Int(f(x), x=0..5280);  value(%);  evalf(%);

>	Int(f(x), x=0..infinity);  value(%);  evalf(%);

Section 7.1 in the MATH-171 Text

Section 6.1 in the Calculus Text: the area between two curves.  6.1: 36

Find the area of the region boxed in by f and g, where  and

>	f := x -> 2-x^2;

>

g := exp;

>	XRG := -2..1:

>	plot([f,g], XRG, colour=[red, black], legend=["f","g"]);

>	A := fsolve(f(x)=g(x), x=-2..-1);

>	B := fsolve(f(x)=g(x), x=0..1);

>	Area := Int( f(x) - g(x), x=A..B);

>

value(%);

>	##########################################

>

>