1040ForShowA27.mws

1040ForShowA27.mws
Thu Oct 27 10:42:41 MDT 2005

>    restart:

Page 98 of our Text -- Integration

Antiderivatives:

>    utah := Int( cos(2*x), x);

utah := Int(cos(2*x),x)

>    value(%);  value(utah);

1/2*sin(2*x)

1/2*sin(2*x)

Maple doesn't do "+ C"

>    wow := Int( exp(-x^2), x);

wow := Int(exp(-x^2),x)

>    value(wow);

1/2*Pi^(1/2)*erf(x)

>    wow := Int( exp( sec(-x^2) ), x);

wow := Int(exp(sec(x^2)),x)

>    value(wow);   Maple says, "I dunno."

int(exp(sec(x^2)),x)

Definite integrals

>    rex := Int( tan(x), x=0..Pi/4);

rex := Int(tan(x),x = 0 .. 1/4*Pi)

>    value(%);

1/2*ln(2)

>    evalf(%);

.3465735903

>    rex := int( tan(x), x=0..Pi/2);

rex := infinity

>    f := x -> exp(-x^2);

f := proc (x) options operator, arrow; exp(-x^2) end proc

We now calculate the area under the graph of f:

>    XRG := -2..3:  plot(f, XRG);

[Maple Plot]

>    Int( f(x), x=XRG);  value(%); evalf(%);

Int(exp(-x^2),x = -2 .. 3)

1/2*erf(2)*Pi^(1/2)+1/2*erf(3)*Pi^(1/2)

1.768288740

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

Int(exp(-x^2),x = 0 .. 5280)

1/2*erf(5280)*Pi^(1/2)

.8862269255

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

Int(exp(-x^2),x = 0 .. infinity)

1/2*Pi^(1/2)

.8862269255

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

>    f := x -> 2-x^2;

f := proc (x) options operator, arrow; 2-x^2 end proc

>    g := exp;

g := exp

>    XRG := -2..2:  YRG := 0..2.1:

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

[Maple Plot]

>    A := fsolve( f(x)=g(x), x=-2..0);

A := -1.315973778

>    B := fsolve( f(x)=g(x), x=0..1);

B := .5372744492

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

Area := Int(2-x^2-exp(x),x = -1.315973778 .. .5372744492)

>    value(%);

1.452013983

>   

>