Thomas Calculus 13th [Solutions]

628 Chapter 8 Techniques of Integration
q6 : Int( f(x,p), x domain );
q7 : value( q6 );
q8 : simplify( q7 ) assuming p -1;
q9 : simplify( q7 ) assuming p -1;
q10 : value( eval( q6, p -1 ) );
i2 : q6 piecewise( p -1, q9, p -1, q10, p -1, q8 );
83. Example CAS commands:
Maple:
f : (x,p) - x^p*ln(x);
domain : 0..infinity;
fn_
list : [seq( f(x,p), p -2..2 )];
plot( fn_
list, x 0..10, y -50..50, color [red,blue,green,cyan,pink], linestyle [1,3,4,7,9],
thickness [3,4,1,2,0], legend ["p -2","p -1","p 0","p 1","p 2"], title "#83 (Section 8.8)" );
q11: Int( f(x,p), x domain ):
q11
``
lhs(i1 i2);
rhs(i1 i2);
`` piecewise( p -1, q4 q9, p -1, q5 q10, p -1, q3 q8 );
`` piecewise( p -1, -infinity, p -1, undefined, p -1, infinity );
84. Example CAS commands:
Maple:
f : (x,p) - x^p*ln(abs(x));
domain : -infinity..infinity;
fn_
list : [seq( f(x,p), p -2..2 )];
plot( fn_
list, x 4..4, y -20..10, color [red,blue,green,cyan,pink], linestyle [1,3,4,7,9],
legend ["p -2","p -1","p 0","p 1","p 2"], title "#84 (Section 8.8)" );
q12 : Int( f(x,p), x domain );
q12p : Int( f(x,p), x 0..infinity );
q12n : Int( f(x,p), x -infinity..0 );
q12 q12p q12n;
`` simplify( q12p q12n );
81-84. Example CAS commands:
Mathematica: (functions and domains may vary)
Clear[x, f, p]
p
f[x _]:
x Log[Abs[x]]
int Integrate[f[x], {x, e, 100)]
int /. p 2.5
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