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LearnCambridge97092026–2027Paper 2 · Pure Mathematics 2Integration

Paper 2 · Module

Integration

4 subtopics≈ 160 min in total

Start the module: Integrating eˣ, 1/x and trigonometric functions Open graphing calculator

Integrating eˣ, 1/x and trigonometric functions
Reversing the new derivatives: $\int e^{ax+b}\,dx$ , $\int\dfrac{1}{ax+b}\,dx$ (the missing case $n=-1$ ), and $\int\sin$ , $\cos$ and $\sec^2$ , always remembering to divide by $a$ .
≈ 40 min
Integration using trigonometric identities
Some trigonometric expressions can't be integrated as they stand. Rewriting them with identities, such as $\cos^2x=\tfrac12(1+\cos2x)$ and $\tan^2x=\sec^2x-1$ , turns them into standard integrals.
≈ 40 min
Exact definite integrals and logarithms
Evaluating definite integrals exactly when the answer involves $e$ , $\ln$ or $\pi$ ; simplifying logarithmic answers; spotting $\dfrac{f'(x)}{f(x)}$ ; and integrating with partial fractions.
≈ 45 min
The trapezium rule
When an integral can't be found exactly, estimate it: replace the curve by straight lines, add up the trapezia, and use the shape of the curve to say whether the answer is too big or too small.
≈ 35 min