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Further calculus formulae

The 4 results the further calculus notes display, each with the conditions it needs to be true and a link to the lesson that states it. Of the 4, the formulae booklet prints 2 and 2 are yours to memorise.

Further Maths · 3 lessons with formulae.

A result the Edexcel formulae booklet prints is marked as such; one it does not print is marked to learn; and a result badged derived in the lesson is a working line the notes build in front of you rather than a standard result to memorise.

3 lessons

Volumes of revolution

V = π \text{∫}_{a}^{b} y^{2} \, dx

NOT IN THE BOOKLET: LEARN ITConditionsA full turn about the x-axis of the region between the curve and that axis, from x = a to x = b. The radius is |y|, so the curve may cross the axis.

Mean values and improper integrals

\text{mean value} = \frac{1}{b - a} \text{∫}_{a}^{b} \text{f}(x) \, dx

NOT IN THE BOOKLET: LEARN ITConditionsb ≠ a, and f integrable across [a, b].

Calculus with inverse trigonometric functions

\frac{d}{dx}(\text{arcsin } x) = \frac{1}{\sqrt{1 - x^{2}}}

IN THE FORMULAE BOOKLETConditions|x| < 1.

\frac{d}{dx}(\text{arctan } x) = \frac{1}{1 + x^{2}}

IN THE FORMULAE BOOKLETConditionsAll x; no restriction.

Every formula in the library is indexed by unit on the equation index, and the further calculus notes are where these results are derived and used. The 2 the booklet does not print are on the list of every formula to memorise, alongside the rest of the course.

Also: Further vectors formulae · Hyperbolic functions formulae