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 $\mathbf {r} =\mathbf {a} +t\mathbf {b}$