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# 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.