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LearnCambridge97092026–2027Paper 1 · Pure Mathematics 1Integration

Paper 1 · Module

Integration

5 subtopics≈ 210 min in total

Start the module: Indefinite integration Open graphing calculator

Indefinite integration
Integration as differentiation in reverse: integrating powers of $x$ , why there is always a $+c$ , and how one point pins down the exact curve.
≈ 40 min
Integrating (ax + b)ⁿ
How to integrate a power of a linear bracket in one step by reversing the chain rule: raise the power, divide by the new power, and divide by the coefficient of $x$ .
≈ 35 min
Definite integrals
What $\displaystyle\int_a^b f(x)\,dx$ means and how to evaluate it, why there is no $+c$ , how to find an unknown limit, and how some integrals with an infinite limit still give a finite answer.
≈ 40 min
Areas under and between curves
Using definite integrals to find areas: under a curve, regions below the axis, between a curve and a line, between two curves, and against the $y$ -axis.
≈ 50 min
Volumes of revolution
Spinning a region around an axis makes a solid. Slicing it into thin discs gives $V=\pi\displaystyle\int y^2\,dx$ about the $x$ -axis and $V=\pi\displaystyle\int x^2\,dy$ about the $y$ -axis, plus regions between two graphs.
≈ 45 min