IB Maths AI 5.6 Definitions

This page contains our IB Maths AI definitions for 5.6. By learning each one of these definitions, you will fully cover the content for IB Maths AI 'Applying integration'.

All Topic 5 Sub-topics 5.1: Introduction To Derivatives 5.2: Applying Derivatives 5.3: Fundamentals Of Integration (HL)5.4: Advanced derivatives (HL)5.5: Further integration (HL)5.6: Applying integration (HL)5.7: Kinematics (HL)5.8: Introduction to differential equations (HL)5.9: Advanced differential equations

disk

Circular cross-section produced when a thin strip is rotated about an axis; its area is $\pi r^2$ , leading to volume integrals of the form $V=\pi \int r^2\,d\left(\text{variable}\right)$ .

radius

The distance from the centre of a circle to any point on the circle.

revolution

Rotation of a planar region around an axis to generate a three-dimensional solid.

shell

Hollow cylindrical layer formed when a vertical strip is rotated about the $y$ -axis; its volume contribution is based on circumference $2\pi x$ times height $f(x)$ and thickness $dx$ .

x-axis

Horizontal coordinate axis used as a line of rotation; distances to it determine radii when using the disk method with

y=f(x)

y-axis

Vertical coordinate axis used as a boundary for area with horizontal strips, or as a line of rotation where radii are measured horizontally.

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