https://touchingfish.top/tags/arc-length/Recent content in Arc-Length on TouchingFish.topHugozh-cnSun, 27 Jun 2021 00:00:00 +0000https://touchingfish.top/calculus101/2021-cal10/Sun, 27 Jun 2021 00:00:00 +0000https://touchingfish.top/calculus101/2021-cal10/<h1 id="体积弧长和表面积">§体积、弧长和表面积</h1> <blockquote> <p>For volumes and surface areas, we&rsquo;ll pay special attention to solids which are formed by revolving a region in the plane about some axis which lies in the plane; such solids are called <em>solids of revolution</em>.</p> </blockquote> <ul> <li>圆盘法（disc method）和壳法（shell method）求体积</li> <li>求更一般固体的体积</li> <li>求光滑曲线（smooth curve）的弧长（arc lengths）和带参数的质点（parametric particles）速率</li> <li>求旋转体（solids of revolution）的表面积</li> </ul> <h2 id="291-旋转体的体积">29.1 旋转体的体积</h2> <p>定积分的回顾（见<em>第16章</em>）</p> <blockquote> <p>So here&rsquo;s the pattern: we make a little strip of width $\mathrm{d}x$ units and height $y$ units at position $x$ on the $x$-axis, work out its area, then put a definite integral sign in front to get the total area we&rsquo;re looking for.</p>