Quote:
Originally posted by HollowTorment
Dial-up is my way to go. It\'s old, slow, and pretty cheap compared to cable and such..well, here anyway.
I\'m -really- cheap. Don\'t say anything clever now..
i1 := Int( cos(2*t), t=0 .. x): i1 = value(i1);
f1 := unapply( value(i1), x ):
p1 := middlebox(cos(2*x), x = 0 .. 5, 25):
p2 := plot( f1(x), x = 0 .. 5, thickness = 2 ):
p3 := plot( cos(2*x), x = -2 .. 6, thickness = 2 ):
plots[display]({p1, p2, p3}, title=`Riemann Sums and Antiderivative` );
i2 := Int(sin(t)^3, t=0 .. x): i2 = `?`;
f2 := unapply( value(i2), x ):
p1 := plot(sin(x)^3, x = -2*Pi .. 2*Pi, thickness = 3):
p2 := middlebox(sin(x)^3, x = -5..5, 60, thickness = 2):
p3 := plot(f2(x), x = -5..5, style=point):
plots[display]({p1, p2, p3}, scaling=constrained);
i3 := Int(sin(t)^3 * cos(t)^4, t=0 .. x): i3 = `?`;
f3 := unapply( value(i3), x ):
p4 := plot(sin(x)^3 * cos(x)^4, x = -Pi .. 2*Pi, thickness = 3):
p5 := middlebox(sin(x)^3 * cos(x)^4, x = 0..5.5, 60, thickness = 2):
p6 := plot(f3(x), x = 0..5.5, style=point):
plots[display]({p4, p5, p6});
Int( cos(2*t), t = 0 .. x);
plot( {sin(x)^2, -cos(2*x)/2}, x = -2*Pi .. 2*Pi, -1 .. 2,
title=`( sin(x) )^2 and -cos(2*x)/2` );
i4 := Int(cos(x)^2, x): i4 = value(i4);
eq0 := sin(x)^2 + cos(x)^2 = 1: eq0, ``;
eq1 := sin(A +

= expand(sin(A + B)): eq1;
eq2 := cos(A +

= expand(cos(A + B)): eq2;
eq3 := subs(A = x, B=x, eq1): eq3;
eq4 := subs(A = x, B=x, eq2): eq4;
eq5 := isolate(eq4, sin(x)^2):
eq6 := isolate(eq0, cos(x)^2):
eq7 := isolate( subs(eq6, eq5), sin(x)^2): eq7;
eq8 := isolate(eq4, cos(x)^2):
eq9 := isolate(eq0, sin(x)^2):
eq10 := isolate(subs(eq9, eq8), cos(x)^2): eq10;
i5 := subs(eq10, i4): i4 = i5; `` = value(i5);
p7 := middlebox(cos(x)^2, x = -1 .. 2.5, 18):
p8 := plot( value(i5), x = -1 .. 2.5, thickness = 2 ):
plots[display]({p7, p8}, title=`Riemann Sums and Antiderivative` );
i6 := Int( sin(x)^2, x):
i7 := subs(eq7, i6): i6 = value(i7);
p9 := middlebox(sin(x)^2, x = -1 .. 5.5, 28):
p10 := plot( value(i6), x = -1 .. 5.5, thickness = 2 ):
p11 := plot(x/2, x = -1 .. 5.5, style=point):
plots[display]({p9, p10, p11}, scaling=constrained,
title=`Riemann Sums and Antiderivative` );
subs(x=t, eq9);
i3 = subs(sin(t)^3=sin(t)*(1 - cos(t)^2), i3);
`` = changevar(cos(t) = u, rhs(\"), u );
`` = expand(rhs(\"));
`` = value(rhs(\"));
i2; plot( {sin^3, f2}, -10 .. 10);
Int(f(u), u);
i8 := Int( sin(x)^4 * cos(x)^5, x): i8; f8 := unapply(value(i8), x):
plot( { sin(x)^4 * cos(x)^5, f8(x) }, x = -10 .. 10);
i9 := Int(sin(x)^2 * cos(x)^2, x):
i9 = subs( eq7, eq10, i9);
`` = simplify( rhs(\"));
`` = subs( subs(x=2*x, eq10), rhs(\"));
`` = value(rhs(\"));