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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.

Curved Square

Stage: 5 Challenge Level: Challenge Level:1
You can solve this using basic properties of areas of circles, coordinate geometry and Pythagoras's theorem or simple trigonometry.
This worksheet suggests a possible method.

You can also solve it using calculus.
This worksheet suggests a possible method.