Integration and Area

Examples 13 and 12

>	with(plots):

Warning, the name changecoords has been redefined

Example 13 and more

>	Int((2*x-4)/(x^3+2*x^2+4*x+8),x);

>

value(%);

>	plot((2*x-4)/(x^3+2*x^2+4*x+8),x=-4..4,y=-10..10,discont=true,thickness=3);

>	plot((2*x-4)/(x^3+2*x^2+4*x+8),x=-1..1,filled=true);

>	-Int((2*x-4)/(x^3+2*x^2+4*x+8),x=-1..1);

>

value(%);

>

evalf(%);

Example 12 and more

>	Int((x+4)/(x^3-3*x^2-4*x+12),x);

>

value(%);

>	plot((x+4)/(x^3-3*x^2-4*x+12),x=-4..4,y=-10..10,discont=true,thickness=3);

>	plot((x+4)/(x^3-3*x^2-4*x+12),x=-1.4..1.4,filled=true);

>	Int((x+4)/(x^3-3*x^2-4*x+12),x=-1.4..1.4);

>

value(%);

>	Int((x+4)/(x^3-3*x^2-4*x+12),x=-7/5..7/5);

>

value(%);

>