IB Maths AA 5.10 Definitions

This page contains our IB Maths AA definitions for 5.10. By learning each one of these definitions, you will fully cover the content for IB Maths AA 'Challenging integration'.

All Topic 5 Sub-topics 5.1: Introduction To Derivatives 5.2: Applying Derivatives 5.3: Advanced Derivatives 5.4: Introduction To Integration 5.5: Advanced Integration 5.6: Kinematics (HL)5.7: Advanced limits (HL)5.8: Implicit differentiation (HL)5.9: Challenging derivatives (HL)5.10: Challenging integration (HL)5.11: Applying integration (HL)5.12: Differential equations (HL)5.13: Maclaurin series

composites

Functions formed by applying one function to the output of another, such as '

f\left(g(x)\right)

', often requiring a chain-rule structure when integrating.

Indefinite integration

Describing an integral that represents a family of antiderivatives and therefore includes an arbitrary constant '

C

integration

The reverse of differentiation, used to rebuild a function from its derivative and to calculate accumulated change such as area.

integration by inspection

Recognising an antiderivative directly by reversing a known derivative pattern, often using the reverse chain rule when the integrand matches '

g'\left(x\right)f\left(g\left(x\right)\right)

integration by parts

A technique for integrating a product by choosing '

u

' and '

dv

' and using '

\int u\,dv=uv-\int v\,du

' to replace the original integral with a simpler one.

integration by substitution

Replacing one expression with another to simplify a differential equation, such as using '

y=vx

' so that '

\frac{dy}{dx}=v+x\frac{dv}{dx}

Repeated integration

Describing applying the same integration method more than once, especially using integration by parts multiple times until the integral can be completed or solved.

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