A-level Mathematics/OCR/C4/Formulae

Formulae
By the end of this module you will be expected to have learnt the following formulae:

Differentiation

 * If $$y = \sin kx,\,$$ then $$\frac{dy}{dx} = k\cos kx$$.
 * If $$y = \cos kx,\,$$ then $$\frac{dy}{dx} = -k\sin kx$$.

Integration

 * $$ \int \cos kx\, dx = \frac{1}{k}\sin kx +c $$
 * $$ \int \sin kx\, dx = -\frac{1}{k}\cos kx +c $$
 * $$ \int f^'[g(x)].g^'(x)\, dx = f[g(x)] +c $$

Vectors

 * $$ \left| x\mathbf{i}+y\mathbf{j}+z\mathbf{k} \right| = \sqrt{x^2+y^2+z^2} $$
 * $$(a\mathbf{i}+b\mathbf{j}+c\mathbf{k})\cdot(x\mathbf{i}+y\mathbf{j}+z\mathbf{k})=ax+by+cz$$
 * $$ \mathbf{a}\cdot\mathbf{b} = \left|\mathbf{a}\right|\left|\mathbf{b}\right|\cos \theta $$
 * The vector equation of a line through point $$\mathbf{a}$$ with direction $$\mathbf{b}$$ is $$\mathbf{r} = \mathbf{a} + t\mathbf{b}$$