  Maple worksheets on applications of integration  Basic calculus topics:

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. Top of page

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