Maple worksheets on applications of integration |

Basic calculus topics:

The following Maple worksheets can be downloaded.

They are all compatible with

Classic Worksheet Maple 10.

Volumes of revolution for the region under a graph-volrev1.mws

- The volume of a cylinder.
- Introductory example .. the volume of a cone.
- A general formula for volumes of solids of revolution.
- Examples.

Volumes of revolution for regions rotated about the y axis-volrev2.mws

- The shell method for determining volumes of revolution.
- Examples.

Volumes of revolution for the region between two curves-volrev3.mws

- The "washer" method for volumes of solids of revolution for the region between two curves.
- The shell method for volumes of solids of revolution for the region between two curves.
- Examples.

Volumes of solids of revolution-revsolid.mws

- The integral formula for the volume of the solid of revolution obtained by rotating a region under a curve about the x axis.
- The integral formula for the volume of the solid of revolution obtained by rotating a region under a curve about the y axis.
- Illustrating solids of revolution and calculating their volumes.
- Solids of revolution obtained by rotating a region between two curves about the x or y axis.
- A procedure for displaying solids of revolution:
revsolid.

Centres of gravity and centroids-centroid.mws

- Moments and centre of gravity.
- The centroid of a triangle.
- The centroid of a region in the coordinate plane by integration.
- Examples of finding centroids.

The centroid of a region between two graphs and Pappus' theorem-centroid2.mws

- The centroid of region between two graphs.
- Examples.
- Pappus' theorem.
- Examples.

Moments of inertia-moment.mws

- Moment of Inertia.
- Moment of inertia of a uniform rod.
- Moment of inertia of a disc.
- Moment of inertia of a rectangular lamina.
- Moment of inertia of a lamina about the x and y axis.
- The perpendicular axis theorem.
- The parallel axis theorem.

The mean and root mean square value of a function on an interval-average.mws

- The mean value of a function on an interval.
- Examples.
- The root mean square value of a function on an interval.
- Examples.

Calculating arc length along a curve-arclength.mws

- The arc length formula.
- Examples.

Calculating the area of a surface of revolution-surfarea.mws

- The area of a cylinder, cone and frustum of a cone or band.
- The area of a surface obtained by rotating a curve around the x axis.
- The area of a surface obtained by rotating a curve around the y axis.
- Examples.

The work done by a force-work.mws

- The work done by a force.
- The work done in extending or compressing a spring.
- Examples.