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.

Integral Equation

Solve this integral equation.

Integral Sandwich

Generalise this inequality involving integrals.

Integral Inequality

Stage: 5 Challenge Level:
Here the first part is a special case of the result in the second part. However it is easier to prove the general case directly.