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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 Inequality

An inequality involving integrals of squares of functions.

Integral Sandwich

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2
This is an example where you have to consider the cases of $n$ even and $n$ odd separately.

The general cases are proved exactly as for parts (i) and (ii) and you may find it easier to consider even values of $n$ first.