Integrals/Integrals.html at master · jes-ka/Integrals · GitHub

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<!DOCTYPE html>
<html lang="en">
	<head>
		<meta charset="utf-8">
		<title>Solving Integrals with Trapezoids</title>
		<meta name="description" content="Finding areas under a curve using trapezoids.">
		<meta name="author" content="Jessica Johnson">

		<!-- Le HTML5 shim, for IE6-8 support of HTML elements -->
		<!--[if lt IE 9]>
		  <script src="http://html5shim.googlecode.com/svn/trunk/html5.js"></script>
		<![endif]-->

		<!-- JQuery -->
		<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.7.1/jquery.min.js"></script>

		<!-- Begin Integral Calculations -->
		<script type="text/javascript">

		/* ----------------------------------------
		 * This method uses trapezoids measure the
		 * area under a curve.
		 *
		 * Delta is how we take into account the
		 * height of each trapezoid, as N is
		 * defined by the user.
		 * ---------------------------------------- */


			function trapezoidFn(a, b, N, func) {
				var delta = (b - a) / N;
				var area = 0.0;

		/* ----------------------------------------
		 * For Loops are usefule with math formulas
		 * because they let us calculate as many
		 * data points as we like by changing N,
		 * the number of iterations.
		 *
		 * A larger N means we will draw smaller
		 * and smaller trapezoids, which gives a
		 * more accurate area under the curve.
		 * ---------------------------------------- */


				for (var i=0; i < N; i++) {
					var y = a + (i * delta);
					var y2 = y + delta;
					area += ((delta / 2) * (func(y) + func(y2)));
				};

				return area;
			}


		/* ----------------------------------------
		 * 			AREA OF A TRAPEZOID
		 *
		 *    A = (height/2) x (base1 + base2)
		 *
		 * Area = half the height of the trapezoid
		 * delta) times the addition of the two
		 * bases (the output for y and y2 of the
		 * curve).
		 * ---------------------------------------- */


		/* These three functions below are defined by the program. */

			function fn3(x) {			/* fn3 simply returns a 3. */
				return 3;
			}

			function fn2(x) {			/* fn2 is a very crazy equation. Answers should get close to 105. */
				return(Math.exp(x) * Math.sqrt(x) * Math.log(x));
			}

			function fn1(x) {			/* fn1 is just x^3, and should get close to 63. */
				return(x*x*x);
			}

		/* End the three defined equations for this program. */

		/* Here is wehre we get the inputed values, and use them for fn1 and fn2. */
			function solveTrap() {
				var aval, bval, nval;
				aval = Number($('#aVal').val());
				bval = Number($('#bVal').val());
				nval = Number($('#nVal').val());

				var returnValue = 'x^3 = ' + trapezoidFn(aval, bval, nval, fn1) + '<br/>exp^x*sqrt x*log x = ' + trapezoidFn(aval, bval, nval, fn2);

				$('#outputLabel').html(returnValue);	/* Get our answer so we can display it to the user. */
			}
		</script>
	</head>

	<body>

<!-- Here is where you ask for input from the user in html format. Make it as pretty as you like! -->

		Lower Limit: <input type="text" name="aVal" id="aVal"></input><br />
		Upper Limit: <input type="text" name="bVal" id="bVal"></input><br />
		Number of Trapezoids: <input type="text" name="nVal" id="nVal"></input><br />
		<button type="button" onclick="solveTrap();">Solve!</button>

		<br /><br />

		<div id="outputLabel"></div>   <!-- Here's the answer. -->

	</body>
</html>