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Area L

Draw the graph of a continuous increasing function in the first quadrant and horizontal and vertical lines through two points. The areas in your sketch lead to a useful formula for finding integrals.

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Integral Equation

Solve this integral equation.

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Integral Sandwich

Generalise this inequality involving integrals.

Integration Matcher

Stage: 5 Challenge Level: Challenge Level:1

The graphs of six functions and the graphs of their integrals have been mixed up below. Can you match them together?




You might also like to use accurate charts suitable for reading off measurements (you will need to print these in landscape mode)

First 6 charts
Second 6 charts

Can you use the charts to estimate the integrals between various points on the graphs of the differentials? Do your estimates match the readings off the graphs of the integrals?

Extension: Can you suggest sensible algebraic forms for the graphs (which are all built from 'standard' functions)