Switched to .xhtml extension, fixed some minor bugs

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diff --git a/project/templates/integral.html b/project/templates/integral.html
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-
-{%- extends "base_math.html" -%}
-
-
-
-{%- block title -%}Area Under the Curve of a Complex Integral{%- endblock -%}
-
-
-
-{%- block style %}
-    <link href="/css/integral.css" rel="stylesheet" />
-{% endblock -%}
-
-
-
-{%- block content %}
-<h4>Area Under the Curve of a Complex Integral</h4>
-
-<p>Scripts used to generate graphs: <a href="/dld/integral_scripts.zip">Link</a></p>
-
-<h5>29/12/2018</h5>
-
-<p>A definite integral can be represented on the xy-plane as the signed area bounded by the curve of
-the function f(x), the x-axis, and the limits of integration a and b. But it's not immediately clear
-how this definition applies for complex valued functions.</p>
-
-<p>Consider the following example:</p>
-
-<div class="precontain"><div class="mathblock">
-    <math xmlns="http://www.w3.org/1998/Math/MathML">
-        <mrow>
-            <munderover>
-                <mo>&#x222b;</mo>
-                <mn>0</mn>
-                <mn>1</mn>
-            </munderover>
-            <msup>
-                <mrow>
-                    <mo>(</mo>
-                    <mn>-1</mn>
-                    <mo>)</mo>
-                </mrow>
-                <mi>x</mi>
-            </msup>
-            <mi>dx</mi>
-        </mrow>
-    </math>
-</div></div>
-
-<p>If the function is graphed on the xy-plane, the real valued outputs are sparse. Yet an elementary
-antiderivative exists and the definite integral is well defined.</p>
-
-<div class="figure">
-    <img src="/img/minus_one_exp_x_real_values_only.png"
-         alt="Real values only plot of minus one raised to the x power"
-         height="400"
-         width="520" />
-    <div class="figcaption">Figure 1 - Real values only</div>
-</div>
-
-<p>In order to plot a meaningful graph that can be used to potentially calculate the integral as a
-signed area, some cues are taken from Philip Lloyd's work on
-<a href="https://phantomgraphs.weebly.com/" class="external">Phantom Graphs</a>. In that work, an
-additional z-axis is used to extend the x-axis into a complex xz-plane, allowing complex inputs to
-be graphed. For the function considered here, the z-axis is instead used to extend the y-axis into a
-complex yz-plane to allow graphing of complex outputs instead.</p>
-
-<p>Upon doing so, the following helical graph is obtained:</p>
-
-<div class="figure">
-    <img src="/img/minus_one_exp_x_full_plot.png"
-         alt="Complete three dimensional graph of all values of minux one raised to the x power"
-         height="400"
-         width="520" />
-    <div class="figcaption">Figure 2 - Full graph</div>
-</div>
-
-<p>The curve is continuous and spirals around the x-axis, intersecting with the real xy-plane at the
-points plotted in the initial graph of Figure 1. However it is still not clear how to represent the
-area under the curve.</p>
-
-<p>Observing that complex numbers in cartesian form are composed of a real part and an imaginary
-part, it is possible to decompose the function into real and imaginary components. These are easy to
-obtain by rotating the graph above to view the real and imaginary parts as flat planes.</p>
-
-<table id="component">
-    <tr>
-        <td>
-            <div class="figure">
-                <img src="/img/cos_pi_x.png"
-                     alt="Graph of the real component of minus one raised to the power of x"
-                     height="400"
-                     width="520" />
-                <div class="figcaption">Figure 3 - Real component</div>
-            </div>
-        </td>
-        <td>
-            <div class="figure">
-                <img src="/img/sin_pi_x.png"
-                     alt="Graph of the imaginary component of minus one raised to the power of x"
-                     height="400"
-                     width="520" />
-                <div class="figcaption">Figure 4 - Imaginary component</div>
-            </div>
-        </td>
-    </tr>
-</table>
-
-<p>From this it can be seen that the function is a combination of a real valued cosine and an
-imaginary valued sine. With the limits of integration under consideration, the real values disappear
-and we are left with the following:</p>
-
-<div class="precontain"><div class="mathblock">
-    <table>
-        <tr>
-            <td colspan="2">
-                <math xmlns="http://www.w3.org/1998/Math/MathML">
-                    <mrow>
-                        <munderover>
-                            <mo>&#x222b;</mo>
-                            <mn>0</mn>
-                            <mn>1</mn>
-                        </munderover>
-                        <msup>
-                            <mrow>
-                                <mo>(</mo>
-                                <mn>-1</mn>
-                                <mo>)</mo>
-                            </mrow>
-                            <mi>x</mi>
-                        </msup>
-                        <mi>dx</mi>
-                    </mrow>
-                </math>
-            </td>
-        </tr>
-        <tr>
-            <td>=</td>
-            <td>
-                <math xmlns="http://www.w3.org/1998/Math/MathML">
-                    <mrow>
-                        <mi>i</mi>
-                        <munderover>
-                            <mo>&#x222b;</mo>
-                            <mn>0</mn>
-                            <mn>1</mn>
-                        </munderover>
-                        <mi>sin</mi>
-                        <mrow>
-                            <mo>(</mo>
-                            <mi>&#x03c0;</mi>
-                            <mo>&#x2062;</mo>
-                            <mi>x</mi>
-                            <mo>)</mo>
-                        </mrow>
-                        <mi>dx</mi>
-                    </mrow>
-                </math>
-            </td>
-        </tr>
-        <tr>
-            <td>=</td>
-            <td>
-                <math xmlns="http://www.w3.org/1998/Math/MathML">
-                    <mrow>
-                        <mo>-</mo>
-                        <mfrac>
-                            <mi>i</mi>
-                            <mi>&#x03c0;</mi>
-                        </mfrac>
-                        <msubsup>
-                            <menclose notation="right">
-                                <mrow>
-                                    <mi>cos</mi>
-                                    <mrow>
-                                        <mo>(</mo>
-                                        <mi>&#x03c0;</mi>
-                                        <mo>&#x2062;</mo>
-                                        <mi>x</mi>
-                                        <mo>)</mo>
-                                    </mrow>
-                                </mrow>
-                            </menclose>
-                            <mn>0</mn>
-                            <mn>1</mn>
-                        </msubsup>
-                    </mrow>
-                </math>
-            </td>
-        </tr>
-        <tr>
-            <td>=</td>
-            <td>
-                <math xmlns="http://www.w3.org/1998/Math/MathML">
-                    <mrow>
-                        <mo>-</mo>
-                        <mfrac>
-                            <mi>i</mi>
-                            <mi>&#x03c0;</mi>
-                        </mfrac>
-                        <mrow>
-                            <mo>(</mo>
-                            <mn>-1</mn>
-                            <mo>-</mo>
-                            <mn>1</mn>
-                            <mo>)</mo>
-                        </mrow>
-                    </mrow>
-                </math>
-            </td>
-        </tr>
-        <tr>
-            <td>=</td>
-            <td>
-                <math xmlns="http://www.w3.org/1998/Math/MathML">
-                    <mrow>
-                        <mfrac>
-                            <mrow>
-                                <mn>2</mn>
-                                <mi>i</mi>
-                            </mrow>
-                            <mi>&#x03c0;</mi>
-                        </mfrac>
-                    </mrow>
-                </math>
-            </td>
-        </tr>
-    </table>
-</div></div>
-
-<p>This agrees with the answer obtained by ordinary evaluation of the integral without considering
-the graph, so the informal area under the curve definition still works. Considering the area under
-the curve using polar coordinates also works, but requires evaluating a less than pleasant infinite
-sum and so won't be considered here.</p>
-
-<p>The next interesting question is how this relates to the surface area of a
-<a href="https://www.mathcurve.com/surfaces.gb/helicoiddroit/helicoiddroit.shtml" class="external">
-right helicoid</a>.</p>
-{% endblock -%}
-
-