Volume with cross section
- $\rhd$ Volume with cross section (5:30) An introduction.
- * Practice: Volumes with cross sections: squares and rectangles (4 problems)
- $\rhd$ Derivatives of inverse functions from tables (5:56) The base of a solid is the region enclosed by the graphs of $y=-x^2+6x-1$ and $y=4$. Cross sections of the solid perpendicular to the $x$-axis are rectangles whose height is $x$. Express the volume of the solid with definite integral.
- $\rhd$ Volume with cross sections perpendicular to y-axis. (4:24) Let $R$ be the region enclosed by $y=4\sqrt{9-x}$ and the axes in the first quadrant. Region $R$ is the base of a solid. For each $y$-value, the cross section of the solid taken perpendicular to the $y$-axis is a rectangle whose base lies in $R$ and whose height is $y$. Express the volume of the solid with a definite integral.
- * Practice: Volumes with cross sections. (4 problems)
Disk method
- $\rhd$ Disk method around the x-axis (9:01) Introduction to the ideas. Use the disk method to find the volume of the solid of revolution generated by rotating the region between the graph of $y=x^2$ and the $x$-axis over the interval $[0,2]$ around the $x$-axis.
- $\rhd$ Disk method around the x-axis (2:34) General formula following the ideas in the previous video.
- $\rhd$ Disk method around the y-axis (7:32) Use the disk method to find the volume of the solid of revolution generated by rotating the region between the graph of $y=x^2$ and the $y$-axis over the interval $[1,4]$ around the $y$-axis.
- * Practice: Disk method around the $x$- or $y$-axis. (4 problems)
Washer method
- $\rhd$ Solid of revolution between two curves (9:06) Find the volume of a solid of revolution formed by revolving the region bounded above by the graph of $y=x$ and $y=\sqrt x$ over the interval $[0,1]$ around the $x$-axis.
- $\rhd$ The washer method (8:06) Generalizing the ideas from the previous video.
- * Practice: Washer method: revolving around $x$- or $y$-axis. (4 problems)
