A level H2 Math preparation tip #2: Integration

  • Integration Techniques

There are lots of formula to remember, but the ones commonly tested are:

a) Trigo: \displaystyle \int{{{{{\sin }}^{2}}{{\theta }_{{}}}d\theta }} (double angle formula)

b) Given in MF 15:

\displaystyle {{\int{{\frac{1}{{{{a}^{2}}+{{x}^{2}}}}}}}_{{}}}dx=\frac{1}{a}{{\tan }^{{-1}}}\left( {\frac{x}{a}} \right)+c

\displaystyle {{\int{{\frac{1}{{\sqrt{{{{a}^{2}}-{{x}^{2}}}}}}}}}_{{}}}dx={{\sin }^{{-1}}}\left( {\frac{x}{a}} \right)+c

int 1

int 2

c) Integration by substitution (same for parametric equations)

int sub 1

d) Integration by parts: \displaystyle \int{{uv'}}=uv-\int{{vu'}}

int parts

e) Partial Fractions

partial frac

  • Area / Volume

It is quite common for questions to calculate area or volume through substitution.

vol

area

  • Differential Equations

Two main types: Story or Non – story. Two general methods: Direct integration or variable separation approach.

It is also common for them to ask for sketches of solution curves and determine if the solution curves approaches or converges to some asymptote.

DE1 DE2 DE3

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