![]() ![]() Alternatively, where each disc has a radius of $f(x)$, the discs approach perfect cylinders as their height $dx$ approaches zero. Goal: To find the volume of a solid using second semester calculus. Summing up all of the areas along the interval gives the total volume. Disc integration, also known in integral calculus as the disc method, is a method for calculating the volume of a solid of revolution of a solid-state material when integrating along an axis 'parallel' to the axis of revolution.This method models the resulting three-dimensional shape as a stack of an infinite number of discs of varying radius and infinitesimal thickness. This will result in creating a 3-D figure whose volume we need to find. Math AP/College Calculus AB Applications of integration Volume with disc method: revolving around other axes Disc method rotation around horizontal line AP Calc: CHA5 (EU), CHA5.C (LO), CHA5.C. Rotate the 2-D function around the given axis Once you graph the function on the 2-D x-y-plane we need to imagine rotating it around the axis given in the problem. Where $R$ is the outer radius (in this case $f(x)$), and $r$ is the inner radius (in this case $g(x)$). Using Wolfram Alpha we can see this graph below. The method can be visualized by considering a thin horizontal rectangle at $y$between $y=f(x)$ on top and $y=g(x)$ on the bottom, and revolving it about the $y$-axis it forms a ring (or disc in the case that $g(x)=0$), with outer radius $f(x)$ and inner radius $g(x)$. Here are 3 steps to using the disk method: Graph the bounded region. Disk Method: Definition, Formula & Examples. Read this guide and also learn the differences between the disk method and the washer method. Integration is along the axis of revolution ( $y$-axis in this case). We find the volume of this disk (ahem, cookie) using our formula from geometry: V ( area of base ) ( width ) V ( R 2) ( w) But this will only give us the volume of one disk (cookie), so we’ll use integration to find the volume of an infinite number of circular cross-sections of the 3D solid. The disk method can be easy to learn and understand.
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