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

$\int \cos kxdx=\frac{1}{k}\sin kx+c$

$\int \sin kxdx=-\frac{1}{k}\cos kx+c$

$\int f^{\text{'}}[g(x)].g^{\text{'}}(x)dx=f[g(x)]+c$

Vectors

$|x𝐢+y𝐣+z𝐤|=\sqrt{x^2+y^2+z^2}$

$(a𝐢+b𝐣+c𝐤)\cdot (x𝐢+y𝐣+z𝐤)=ax+by+cz$

$𝐚\cdot 𝐛=\left|𝐚\right|\left|𝐛\right|\cos \theta$

The vector equation of a line through point $𝐚$ with direction $𝐛$ is $𝐫=𝐚+t𝐛$