Definite integrals in engineering
A collection of resources to provide ideas for setting definite integrals in the context of engineering, together with materials to support teaching of these topics.
'Gas Compression and Expansion' looks at calculating the energy used when the volume of a gas changes. An interactive file graphs the motion of a piston in a cylinder. The mathematics is focussed on definite integrals.
There are two supporting resources. 'Thinking Questions' is a resource from Susan Wall that includes material on definite integrals. 'Risps for A2 Level Core: Integration 2' gives an area bounded by two functions and poses the question as to what functions bound the area?
Gas Compression and Expansion
How can you calculate the energy used, or made available, when the volume of a gas is changed? A bicycle pump, a refrigerator and the internal combustion engine change the volume of a gas or a liquid. Boyle’s law is used and students need to be able to integrate to complete the activities. Isothermal change and adiabatic change are considered. An interactive file graphs the motion of a piston in a cylinder. The mathematics covered in this resource is to distinguish between definite and indefinite integrals, in addition to interpreting data.
Thinking Questions
This resource from Susan Wall contains a number of open–ended questions which explore understanding and allow a variety of approaches. There is a resource specific to exploring integration between limits.
Risps for A2 Level Core: Integration 2
This resource looks at shaded area, gives the area, and asks the question 'what are the functions'. Solving the problem draws in work on the Trapezium Rule and investigations using volumes of revolution.
