Following toggle tip provides clarification

# Integration (Metric)

Learn, or revise, techniques of integration (parts, substitution, partial fractions, reduction formulae) and applications to areas in the plane and volumes of revolution.

## Units

### Techniques

Integration by parts, by substitution and with the use of partial fractions (A-level topics); improper integrals and reduction formulae (Further Maths topics).

The use of the formula \(\int u\,dv=u\,v-\int v\,du\).

Integration using substitution, or change of variable.

Integration of rational functions by reducing them to partial fractions.

Integrals between \(a\) and \(\infty\); convergence and non-convergence.

Integration of \(I_n=\int f_n(x)\,dx\) by expression \(I_n\) in terms of \(I_{n-1}\) or \(I_{n-2}\).

### Applications

Areas between curves, and volumes of revolution. This is an A-level topic, which Science and Engineering courses at Imperial will assume you know.

Area enclosed by the intersecting curves \(y=f(x)\) and \(y=g(x)\).

Volume of revolution about the \(x\)- and \(y\)-axis.