test_defint = ->
	run_test [
		"defint(x^2,y,0,sqrt(1-x^2),x,-1,1)",
		"1/8*pi",

		# from the eigenmath manual

		"z=2",
		"",

		"P=(x,y,z)",
		"",

		"a=abs(cross(d(P,x),d(P,y)))",
		"",

		"defint(a,y,-sqrt(1-x^2),sqrt(1-x^2),x,-1,1)",
		"pi",

		# from the eigenmath manual

		"z=x^2+2y",
		"",

		"P=(x,y,z)",
		"",

		"a=abs(cross(d(P,x),d(P,y)))",
		"",

		"defint(a,x,0,1,y,0,1)",
		"3/2+5/8*log(5)",

		# from the eigenmath manual

		"x=u*cos(v)",
		"",

		"y=u*sin(v)",
		"",

		"z=v",
		"",

		"S=(x,y,z)",
		"",

		"a=abs(cross(d(S,u),d(S,v)))",
		"",

		"defint(a,u,0,1,v,0,3pi)",
		"3/2*pi*log(1+2^(1/2))+3*pi/(2^(1/2))",
	]