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Integration (Metric)

Class Details

Tom Baker

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).

Integration by Inspection
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Lesson Not yet graded
Integration by Parts
Resume

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

Lesson Not yet graded
Integration by Substitution
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Integration using substitution, or change of variable.

Lesson 0.0 / 6.0 (0.0%)
Use of Partial Fractions
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Integration of rational functions by reducing them to partial fractions.

Lesson Not yet graded
Improper Integrals
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Integrals between \(a\) and \(\infty\); convergence and non-convergence.

Lesson Not yet graded
Reduction Formulae
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Integration of \(I_n=\int f_n(x)\,dx\) by expression \(I_n\) in terms of \(I_{n-1}\) or \(I_{n-2}\).

Lesson Not yet graded

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.

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