Solving the second problem of calculus with Ruby!

[Ryex]

So... when I realized how to theoretically solve for the area under a curve I endeavored to make a ruby program to automate the process
and here was the result

link to the .rb file
http://docs.google.com/leaf?id=0B0KLI9M5vfiOZDI4OGIyMzktYTA5Mi00YTMyLTlhMGMtODQxOGVjNTcwNTc1&hl=en
link to a no ruby required .exe
http://www.mediafire.com/?wlzngwnotww
source code

def auc
   its = ac = x2 = x1 = nil
	puts 'start point of domain:'
	x1 = gets
	x1 = x1.to_i
	puts 'end point of domain:'
	x2 = gets
	x2 = x2.to_i
	puts 'accuracy:'
	ac = gets	
	ac = ac.to_i
	puts 'solving...'
	w = 1
	area = 0
	last_area = 0
	i1 = 0
	x = x1
	loop do
		area = 0
		a=(1.0/(10)**i1)
		(((x2 - x1) / a).floor).times { |i2|
			fx = yield(x + (i2 * a))
			box = fx * a
			area += box
		}
		unless i1 == 0
			difference = area - last_area

			last_area = area
			break if difference.abs <= (1*(10**(-ac)))
		end
		i1 += 1
		puts 'iteration: ' + i1.to_s + 'Compleate...'
	end
	puts  '-----------------------------------------------------------'
	puts 'area: ' + area.to_s
	puts 'iterations: ' + (i1 + 1).to_s
	puts  '-----------------------------------------------------------'
	puts 'type \'exit\' to close, or press enter to continue with another function'
	s = gets
	case s.upcase
	when /\AEXIT/
		exit
	else
		start_program
	end
end

def start_program
	puts '=============================================='
	puts 'Welcome to the area under a curve calculus solver'
	puts 'to use simply type you function in below and then follow the prompts'
	puts 'for exsample '
	puts '((-x)**2) + 2'
	puts 'Would be the function x^2 + 2'
	puts 'the solver only recognises certain symbols for mathmatical'
	puts 'operations, see the below for conversions'
	puts 'make sure to use \"X\" when typeing in your equation'
	puts '* >> Multiplication'
	puts '** >> raise to a power '
	puts '/ >> Division '
	puts 'Math.cos(x) >> Cosine of x '
	puts 'Math.sin(x) >> Sine of x '
	puts 'Math.tan(x) >> Tangent of x '
	puts 'Math.log(x) >> Ln of x '
	puts 'Math.log10(x) >> Log base 10 of x '
	puts 'Math.sqrt(x) >> Square root of x '
	puts '(x).abs >> Absolute value of '
	puts 'Math::E >> e '
	puts 'Math::PI >> pi '
	puts '=============================================='
	puts 'type \'exit\' to close'
	puts 'type your function below'
	no_input = true
	while no_input == true
		s = gets
		case s.upcase
		when ''
			puts 'ERROR Please enter a function'
		when /\AEXIT/
			puts 'Closing...'
			exit
		else
			no_input  = false
		end
	end
	f = 'auc{|x| ' + s.to_s + '}'
	begin
		eval(f)
	rescue 
		puts 'ERROR'
		puts $!.message
	end
end

begin
	start_program
end

note that if you are using a domain that is in any way large it will take a very long time depending of the number you put in for accuracy
a domain of 10 and an accuracy of 3  took a while (a testament to the slowness of ruby)

I was really proud of my self for making this in less than 3 hours (that includes looking up blocks something I didn't previously know how to use) .

[fugibo]

Ick! You used the box method. I hate that silly thing. Even though it's exactly the same as the integration method, I still hate it. Grr.

Also, after spending five seconds looking over it, it looks like you're using a rather imprecise method. I'm afraid this just won't work well without the fundamental theorem or limits, neither of which can be easily emulated in Ruby.

[Ryex]

well keep in mind that we were only given the problem to solve today.
(the teacher hasn't even gone over how to officially solve it yet)
I just did my best to create a loop method that would get the same effect as the limit as a approaches 0 of the summation of the area off all the boxes with width a the fit under the curve.
it's the only way I could think to solve it.

and how is it imprecise? it's results can be accurate to what ever place you want, thought considering the speed of the method I wouldn't suggest asking for an accuracy beyond 5. you will be waiting a while if you do.

I made this more to test my self and see it I COULD make, not so much to really use it. just an atempt to se if I could apply way I knew of ruby and the math behind this particular problem.

so what is this "integration method" you speak of?

[winkio]

cool that you built it, but not really mathematically useful.  If you want to improve it, use trapezoids instead of boxes, or other even more precise methods if you wish.

Integration is Calculus, you will learn about it.

[fugibo]

The real solution to the problem is incredibly easy. The way they teach this crap to you is ridiculous. Integration is the opposite of derivation. You use it to find a function for f(x) that's derivative is f(x). Since the function is the sum of the slope of f(x) at each point, it automatically acts as an area function. You can derive a lot of the stuff you're probably going to spend the next week on by yourself if you try.

[Ryex]

cool that you built it, but not really mathematically useful.

you can say that again, it lags like hell.

[fugibo]

cool that you built it, but not really mathematically useful.

you can say that again, it lags like hell.

I'm pretty sure even a native implementation would have a decent amount of lag. This is why we created the fundamental theorem. Iteration just doesn't work without an extraordinarily fast computer.