test.ipynb

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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "$$ V = \\int_0^{\\sqrt{\\frac{\\pi}{2}}}{2\\pi*4x\\sin{2x^2}}dx $$"
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "$u$ Subsitution"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Let:\n$$ u = x^2, du=2xdx $$"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "$$ V = \\int_{0}^{\\sqrt{\\frac{\\pi}{2}}}{2\\pi\\sin({2(x^2)})2(2xdx)} = \\int_{0}^{\\sqrt{\\frac{\\pi}{2}}}{2\\pi\\sin{(2(u))}2(du)} $$"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Pull out constants:\n$$ V = 4\\pi \\int_{0}^{\\sqrt{\\frac{\\pi}{2}}}{sin{(2u)}du} $$"
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "Integration of $u$"
    },
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     "metadata": {},
     "source": ""
    }
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   "metadata": {}
  }
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