Integration

3.5

What the syllabus asks of you

extend the idea of ‘reverse differentiation’ to include the integration of e^(ax + b), 1/(ax + b), sin(ax + b), cos(ax + b), sec²(ax + b) and 1/(x² + a²)
use trigonometrical relationships in carrying out integration
integrate rational functions by means of decomposition into partial fractions
recognise an integrand of the form kf′(x)/f(x), and integrate such functions
recognise when an integrand can usefully be regarded as a product, and use integration by parts
use a given substitution to simplify and evaluate either a definite or an indefinite integral.

Read the notes first

Chapter 13: Further integration

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Drill this topic

All 50 questions on Integration, untimed — answer on paper, then mark yourself against the mark scheme.

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Make a worksheet

Choose the years and how many questions, then print it with the answers on separate pages.

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50 questions

These are structured questions, answered in working rather than by picking an option, so they are not listed here one by one. The drill above puts each in front of you with its mark scheme to check against.