Edexcel IGCSE·Further Pure Mathematics·IGCSE Further Pure Mathematics

Integration

13 min read

Integrating powers, the constant of integration, definite integrals and the area under a curve.

Integration reverses differentiation and finds areas under curves.

The rule for powers

$\int x^n \, dx = \frac{x^{n+1}}{n+1} + c \quad (n \neq -1)$ Add one to the power, divide by the new power, and add $+c$ for an indefinite integral.

Worked example. $\int (6x^2 - 4x + 1)\,dx = 2x^3 - 2x^2 + x + c$

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Edexcel IGCSE·Further Pure Mathematics·IGCSE Further Pure Mathematics

13 min read

Integrating powers, the constant of integration, definite integrals and the area under a curve.

Integration reverses differentiation and finds areas under curves.

$\int x^n \, dx = \frac{x^{n+1}}{n+1} + c \quad (n \neq -1)$ Add one to the power, divide by the new power, and add $+c$ for an indefinite integral.

Worked example. $\int (6x^2 - 4x + 1)\,dx = 2x^3 - 2x^2 + x + c$

Create a free account to read this note in full. Every free account gets 2 complete revision notes — no card needed.